GCSE Maths Units and Compound Measures (Higher): worked examples and questions with answers

Key words. A unit is a standard size we measure in. Metres and centimetres measure the same kind of thing, but one is bigger than the other.

Method. To change units, use the fact that links them. Changing to a smaller unit means a bigger number (multiply); changing to a bigger unit means a smaller number (divide).

1. Decide what should happen to the number: metres to centimetres. Metres are the bigger unit and centimetres are the smaller unit, so it takes more centimetres to make the same amount. We expect the number to get bigger.
   3 m → ? cm
2. Change metres to centimetres. Use the fact 1 m = 100 cm. Each metre is 100 cm, so you need 100 times as many centimetres as metres. The centimetre is the smaller unit, so the number gets bigger: multiply by 100.
   3 × 100 = 300 cm
3. Write the answer with its unit. Always finish by writing the new unit.
   3 m = 300 cm

Check. Convert back: 300 cm gives 3 m (300 ÷ 100 = 3). ✓

Watch out. Ask yourself: will the number get bigger or smaller? Metres to centimetres: you get more of the smaller unit, so the number grows.

Key words. A unit is a standard size we measure in. Centimetres and metres measure the same kind of thing, but one is bigger than the other.

Method. To change units, use the fact that links them. Changing to a smaller unit means a bigger number (multiply); changing to a bigger unit means a smaller number (divide).

1. Decide what should happen to the number: centimetres to metres. Centimetres are the smaller unit and metres are the bigger unit, so it takes fewer metres to make the same amount. We expect the number to get smaller.
   450 cm → ? m
2. Change centimetres to metres. Use the fact 1 m = 100 cm. It takes 100 centimetres to make one metre, so you need 100 times fewer metres than centimetres. The metre is the bigger unit, so the number gets smaller: divide by 100.
   450 ÷ 100 = 4.5 m
3. Write the answer with its unit. Always finish by writing the new unit.
   450 cm = 4.5 m

Check. Convert back: 4.5 m gives 450 cm (4.5 × 100 = 450). ✓

Watch out. Ask yourself: will the number get bigger or smaller? Metres to centimetres: you get more of the smaller unit, so the number grows.

Key words. A unit is a standard size we measure in. Kilometres and metres measure the same kind of thing, but one is bigger than the other.

Method. To change units, use the fact that links them. Changing to a smaller unit means a bigger number (multiply); changing to a bigger unit means a smaller number (divide).

1. Decide what should happen to the number: kilometres to metres. Kilometres are the bigger unit and metres are the smaller unit, so it takes more metres to make the same amount. We expect the number to get bigger.
   2.5 km → ? m
2. Change kilometres to metres. Use the fact 1 km = 1000 m. Each kilometre is 1000 m, so you need 1000 times as many metres as kilometres. The metre is the smaller unit, so the number gets bigger: multiply by 1000.
   2.5 × 1000 = 2500 m
3. Write the answer with its unit. Always finish by writing the new unit.
   2.5 km = 2500 m

Check. Convert back: 2500 m gives 2.5 km (2500 ÷ 1000 = 2.5). ✓

Watch out. Ask yourself: will the number get bigger or smaller? Metres to centimetres: you get more of the smaller unit, so the number grows.

Key words. A unit is a standard size we measure in. Metres and kilometres measure the same kind of thing, but one is bigger than the other.

Method. To change units, use the fact that links them. Changing to a smaller unit means a bigger number (multiply); changing to a bigger unit means a smaller number (divide).

1. Decide what should happen to the number: metres to kilometres. Metres are the smaller unit and kilometres are the bigger unit, so it takes fewer kilometres to make the same amount. We expect the number to get smaller.
   6000 m → ? km
2. Change metres to kilometres. Use the fact 1 km = 1000 m. It takes 1000 metres to make one kilometre, so you need 1000 times fewer kilometres than metres. The kilometre is the bigger unit, so the number gets smaller: divide by 1000.
   6000 ÷ 1000 = 6 km
3. Write the answer with its unit. Always finish by writing the new unit.
   6000 m = 6 km

Check. Convert back: 6 km gives 6000 m (6 × 1000 = 6000). ✓

Watch out. Ask yourself: will the number get bigger or smaller? Metres to centimetres: you get more of the smaller unit, so the number grows.

Key words. A unit is a standard size we measure in. Centimetres and millimetres measure the same kind of thing, but one is bigger than the other.

Method. To change units, use the fact that links them. Changing to a smaller unit means a bigger number (multiply); changing to a bigger unit means a smaller number (divide).

1. Decide what should happen to the number: centimetres to millimetres. Centimetres are the bigger unit and millimetres are the smaller unit, so it takes more millimetres to make the same amount. We expect the number to get bigger.
   8 cm → ? mm
2. Change centimetres to millimetres. Use the fact 1 cm = 10 mm. Each centimetre is 10 mm, so you need 10 times as many millimetres as centimetres. The millimetre is the smaller unit, so the number gets bigger: multiply by 10.
   8 × 10 = 80 mm
3. Write the answer with its unit. Always finish by writing the new unit.
   8 cm = 80 mm

Check. Convert back: 80 mm gives 8 cm (80 ÷ 10 = 8). ✓

Watch out. Ask yourself: will the number get bigger or smaller? Metres to centimetres: you get more of the smaller unit, so the number grows.

Key words. A unit is a standard size we measure in. Millimetres and centimetres measure the same kind of thing, but one is bigger than the other.

Method. To change units, use the fact that links them. Changing to a smaller unit means a bigger number (multiply); changing to a bigger unit means a smaller number (divide).

1. Decide what should happen to the number: millimetres to centimetres. Millimetres are the smaller unit and centimetres are the bigger unit, so it takes fewer centimetres to make the same amount. We expect the number to get smaller.
   35 mm → ? cm
2. Change millimetres to centimetres. Use the fact 1 cm = 10 mm. It takes 10 millimetres to make one centimetre, so you need 10 times fewer centimetres than millimetres. The centimetre is the bigger unit, so the number gets smaller: divide by 10.
   35 ÷ 10 = 3.5 cm
3. Write the answer with its unit. Always finish by writing the new unit.
   35 mm = 3.5 cm

Check. Convert back: 3.5 cm gives 35 mm (3.5 × 10 = 35). ✓

Watch out. Ask yourself: will the number get bigger or smaller? Metres to centimetres: you get more of the smaller unit, so the number grows.

Key words. A unit is a standard size we measure in. Kilograms and grams measure the same kind of thing, but one is bigger than the other.

Method. To change units, use the fact that links them. Changing to a smaller unit means a bigger number (multiply); changing to a bigger unit means a smaller number (divide).

1. Decide what should happen to the number: kilograms to grams. Kilograms are the bigger unit and grams are the smaller unit, so it takes more grams to make the same amount. We expect the number to get bigger.
   4 kg → ? g
2. Change kilograms to grams. Use the fact 1 kg = 1000 g. Each kilogram is 1000 g, so you need 1000 times as many grams as kilograms. The gram is the smaller unit, so the number gets bigger: multiply by 1000.
   4 × 1000 = 4000 g
3. Write the answer with its unit. Always finish by writing the new unit.
   4 kg = 4000 g

Check. Convert back: 4000 g gives 4 kg (4000 ÷ 1000 = 4). ✓

Watch out. Ask yourself: will the number get bigger or smaller? Metres to centimetres: you get more of the smaller unit, so the number grows.

Key words. A unit is a standard size we measure in. Grams and kilograms measure the same kind of thing, but one is bigger than the other.

Method. To change units, use the fact that links them. Changing to a smaller unit means a bigger number (multiply); changing to a bigger unit means a smaller number (divide).

1. Decide what should happen to the number: grams to kilograms. Grams are the smaller unit and kilograms are the bigger unit, so it takes fewer kilograms to make the same amount. We expect the number to get smaller.
   3500 g → ? kg
2. Change grams to kilograms. Use the fact 1 kg = 1000 g. It takes 1000 grams to make one kilogram, so you need 1000 times fewer kilograms than grams. The kilogram is the bigger unit, so the number gets smaller: divide by 1000.
   3500 ÷ 1000 = 3.5 kg
3. Write the answer with its unit. Always finish by writing the new unit.
   3500 g = 3.5 kg

Check. Convert back: 3.5 kg gives 3500 g (3.5 × 1000 = 3500). ✓

Watch out. Ask yourself: will the number get bigger or smaller? Metres to centimetres: you get more of the smaller unit, so the number grows.

Key words. A unit is a standard size we measure in. Tonnes and kilograms measure the same kind of thing, but one is bigger than the other.

Method. To change units, use the fact that links them. Changing to a smaller unit means a bigger number (multiply); changing to a bigger unit means a smaller number (divide).

1. Decide what should happen to the number: tonnes to kilograms. Tonnes are the bigger unit and kilograms are the smaller unit, so it takes more kilograms to make the same amount. We expect the number to get bigger.
   2 tonnes → ? kg
2. Change tonnes to kilograms. Use the fact 1 tonne = 1000 kg. Each tonne is 1000 kg, so you need 1000 times as many kilograms as tonnes. The kilogram is the smaller unit, so the number gets bigger: multiply by 1000.
   2 × 1000 = 2000 kg
3. Write the answer with its unit. Always finish by writing the new unit.
   2 tonnes = 2000 kg

Check. Convert back: 2000 kg gives 2 tonnes (2000 ÷ 1000 = 2). ✓

Watch out. Ask yourself: will the number get bigger or smaller? Metres to centimetres: you get more of the smaller unit, so the number grows.

Key words. A unit is a standard size we measure in. Kilograms and tonnes measure the same kind of thing, but one is bigger than the other.

Method. To change units, use the fact that links them. Changing to a smaller unit means a bigger number (multiply); changing to a bigger unit means a smaller number (divide).

1. Decide what should happen to the number: kilograms to tonnes. Kilograms are the smaller unit and tonnes are the bigger unit, so it takes fewer tonnes to make the same amount. We expect the number to get smaller.
   7500 kg → ? tonnes
2. Change kilograms to tonnes. Use the fact 1 tonne = 1000 kg. It takes 1000 kilograms to make one tonne, so you need 1000 times fewer tonnes than kilograms. The tonne is the bigger unit, so the number gets smaller: divide by 1000.
   7500 ÷ 1000 = 7.5 tonnes
3. Write the answer with its unit. Always finish by writing the new unit.
   7500 kg = 7.5 tonnes

Check. Convert back: 7.5 tonnes gives 7500 kg (7.5 × 1000 = 7500). ✓

Watch out. Ask yourself: will the number get bigger or smaller? Metres to centimetres: you get more of the smaller unit, so the number grows.

Key words. A unit is a standard size we measure in. Kilograms and grams measure the same kind of thing, but one is bigger than the other.

Method. To change units, use the fact that links them. Changing to a smaller unit means a bigger number (multiply); changing to a bigger unit means a smaller number (divide).

1. Decide what should happen to the number: kilograms to grams. Kilograms are the bigger unit and grams are the smaller unit, so it takes more grams to make the same amount. We expect the number to get bigger.
   0.6 kg → ? g
2. Change kilograms to grams. Use the fact 1 kg = 1000 g. Each kilogram is 1000 g, so you need 1000 times as many grams as kilograms. The gram is the smaller unit, so the number gets bigger: multiply by 1000.
   0.6 × 1000 = 600 g
3. Write the answer with its unit. Always finish by writing the new unit.
   0.6 kg = 600 g

Check. Convert back: 600 g gives 0.6 kg (600 ÷ 1000 = 0.6). ✓

Watch out. Ask yourself: will the number get bigger or smaller? Metres to centimetres: you get more of the smaller unit, so the number grows.

Key words. A unit is a standard size we measure in. Grams and kilograms measure the same kind of thing, but one is bigger than the other.

Method. To change units, use the fact that links them. Changing to a smaller unit means a bigger number (multiply); changing to a bigger unit means a smaller number (divide).

1. Decide what should happen to the number: grams to kilograms. Grams are the smaller unit and kilograms are the bigger unit, so it takes fewer kilograms to make the same amount. We expect the number to get smaller.
   450 g → ? kg
2. Change grams to kilograms. Use the fact 1 kg = 1000 g. It takes 1000 grams to make one kilogram, so you need 1000 times fewer kilograms than grams. The kilogram is the bigger unit, so the number gets smaller: divide by 1000.
   450 ÷ 1000 = 0.45 kg
3. Write the answer with its unit. Always finish by writing the new unit.
   450 g = 0.45 kg

Check. Convert back: 0.45 kg gives 450 g (0.45 × 1000 = 450). ✓

Watch out. Ask yourself: will the number get bigger or smaller? Metres to centimetres: you get more of the smaller unit, so the number grows.

Key words. A unit is a standard size we measure in. Litres and millilitres measure the same kind of thing, but one is bigger than the other.

Method. To change units, use the fact that links them. Changing to a smaller unit means a bigger number (multiply); changing to a bigger unit means a smaller number (divide).

1. Decide what should happen to the number: litres to millilitres. Litres are the bigger unit and millilitres are the smaller unit, so it takes more millilitres to make the same amount. We expect the number to get bigger.
   3 litres → ? ml
2. Change litres to millilitres. Use the fact 1 litre = 1000 ml. Each litre is 1000 ml, so you need 1000 times as many millilitres as litres. The millilitre is the smaller unit, so the number gets bigger: multiply by 1000.
   3 × 1000 = 3000 ml
3. Write the answer with its unit. Always finish by writing the new unit.
   3 litres = 3000 ml

Check. Convert back: 3000 ml gives 3 litres (3000 ÷ 1000 = 3). ✓

Watch out. Ask yourself: will the number get bigger or smaller? Metres to centimetres: you get more of the smaller unit, so the number grows.

Key words. A unit is a standard size we measure in. Millilitres and litres measure the same kind of thing, but one is bigger than the other.

Method. To change units, use the fact that links them. Changing to a smaller unit means a bigger number (multiply); changing to a bigger unit means a smaller number (divide).

1. Decide what should happen to the number: millilitres to litres. Millilitres are the smaller unit and litres are the bigger unit, so it takes fewer litres to make the same amount. We expect the number to get smaller.
   4500 ml → ? litres
2. Change millilitres to litres. Use the fact 1 litre = 1000 ml. It takes 1000 millilitres to make one litre, so you need 1000 times fewer litres than millilitres. The litre is the bigger unit, so the number gets smaller: divide by 1000.
   4500 ÷ 1000 = 4.5 litres
3. Write the answer with its unit. Always finish by writing the new unit.
   4500 ml = 4.5 litres

Check. Convert back: 4.5 litres gives 4500 ml (4.5 × 1000 = 4500). ✓

Watch out. Ask yourself: will the number get bigger or smaller? Metres to centimetres: you get more of the smaller unit, so the number grows.

Key words. A unit is a standard size we measure in. Centilitres and litres measure the same kind of thing, but one is bigger than the other.

Method. To change units, use the fact that links them. Changing to a smaller unit means a bigger number (multiply); changing to a bigger unit means a smaller number (divide).

1. Decide what should happen to the number: centilitres to litres. Centilitres are the smaller unit and litres are the bigger unit, so it takes fewer litres to make the same amount. We expect the number to get smaller.
   250 cl → ? litres
2. Change centilitres to litres. Use the fact 1 litre = 100 cl. It takes 100 centilitres to make one litre, so you need 100 times fewer litres than centilitres. The litre is the bigger unit, so the number gets smaller: divide by 100.
   250 ÷ 100 = 2.5 litres
3. Write the answer with its unit. Always finish by writing the new unit.
   250 cl = 2.5 litres

Check. Convert back: 2.5 litres gives 250 cl (2.5 × 100 = 250). ✓

Watch out. Ask yourself: will the number get bigger or smaller? Metres to centimetres: you get more of the smaller unit, so the number grows.

Key words. A unit is a standard size we measure in. Litres and centilitres measure the same kind of thing, but one is bigger than the other.

Method. To change units, use the fact that links them. Changing to a smaller unit means a bigger number (multiply); changing to a bigger unit means a smaller number (divide).

1. Decide what should happen to the number: litres to centilitres. Litres are the bigger unit and centilitres are the smaller unit, so it takes more centilitres to make the same amount. We expect the number to get bigger.
   1.5 litres → ? cl
2. Change litres to centilitres. Use the fact 1 litre = 100 cl. Each litre is 100 cl, so you need 100 times as many centilitres as litres. The centilitre is the smaller unit, so the number gets bigger: multiply by 100.
   1.5 × 100 = 150 cl
3. Write the answer with its unit. Always finish by writing the new unit.
   1.5 litres = 150 cl

Check. Convert back: 150 cl gives 1.5 litres (150 ÷ 100 = 1.5). ✓

Watch out. Ask yourself: will the number get bigger or smaller? Metres to centimetres: you get more of the smaller unit, so the number grows.

Key words. A unit is a standard size we measure in. Centilitres and millilitres measure the same kind of thing, but one is bigger than the other.

Method. To change units, use the fact that links them. Changing to a smaller unit means a bigger number (multiply); changing to a bigger unit means a smaller number (divide).

1. Decide what should happen to the number: centilitres to millilitres. Centilitres are the bigger unit and millilitres are the smaller unit, so it takes more millilitres to make the same amount. We expect the number to get bigger.
   8 cl → ? ml
2. Change centilitres to millilitres. Use the fact 1 cl = 10 ml. Each centilitre is 10 ml, so you need 10 times as many millilitres as centilitres. The millilitre is the smaller unit, so the number gets bigger: multiply by 10.
   8 × 10 = 80 ml
3. Write the answer with its unit. Always finish by writing the new unit.
   8 cl = 80 ml

Check. Convert back: 80 ml gives 8 cl (80 ÷ 10 = 8). ✓

Watch out. Ask yourself: will the number get bigger or smaller? Metres to centimetres: you get more of the smaller unit, so the number grows.

Key words. A unit is a standard size we measure in. Millilitres and centilitres measure the same kind of thing, but one is bigger than the other.

Method. To change units, use the fact that links them. Changing to a smaller unit means a bigger number (multiply); changing to a bigger unit means a smaller number (divide).

1. Decide what should happen to the number: millilitres to centilitres. Millilitres are the smaller unit and centilitres are the bigger unit, so it takes fewer centilitres to make the same amount. We expect the number to get smaller.
   90 ml → ? cl
2. Change millilitres to centilitres. Use the fact 1 cl = 10 ml. It takes 10 millilitres to make one centilitre, so you need 10 times fewer centilitres than millilitres. The centilitre is the bigger unit, so the number gets smaller: divide by 10.
   90 ÷ 10 = 9 cl
3. Write the answer with its unit. Always finish by writing the new unit.
   90 ml = 9 cl

Check. Convert back: 9 cl gives 90 ml (9 × 10 = 90). ✓

Watch out. Ask yourself: will the number get bigger or smaller? Metres to centimetres: you get more of the smaller unit, so the number grows.

Key words. A unit is a standard size we measure in. Kilometres and centimetres measure the same kind of thing, but one is bigger than the other.

Method. To change units, use the fact that links them. Changing to a smaller unit means a bigger number (multiply); changing to a bigger unit means a smaller number (divide).

1. Decide what should happen to the number: kilometres to centimetres. Kilometres are the bigger unit and centimetres are the smaller unit, so it takes more centimetres to make the same amount. We expect the number to get bigger.
   0.4 km → ? cm
2. Change kilometres to metres. Use the fact 1 km = 1000 m. Each kilometre is 1000 m, so you need 1000 times as many metres as kilometres. The metre is the smaller unit, so the number gets bigger: multiply by 1000.
   0.4 × 1000 = 400 m
3. Change metres to centimetres. Use the fact 1 m = 100 cm. Each metre is 100 cm, so you need 100 times as many centimetres as metres. The centimetre is the smaller unit, so the number gets bigger: multiply by 100.
   400 × 100 = 40,000 cm
4. Write the answer with its unit. We went one unit at a time so each step uses a fact you already know.
   0.4 km = 40,000 cm

Check. Convert back: 40,000 cm gives 0.4 km (40,000 ÷ 100,000 = 0.4). ✓

Watch out. Ask yourself: will the number get bigger or smaller? Metres to centimetres: you get more of the smaller unit, so the number grows.

Key words. A unit is a standard size we measure in. Tonnes and grams measure the same kind of thing, but one is bigger than the other.

Method. To change units, use the fact that links them. Changing to a smaller unit means a bigger number (multiply); changing to a bigger unit means a smaller number (divide).

1. Decide what should happen to the number: tonnes to grams. Tonnes are the bigger unit and grams are the smaller unit, so it takes more grams to make the same amount. We expect the number to get bigger.
   0.02 tonnes → ? g
2. Change tonnes to kilograms. Use the fact 1 tonne = 1000 kg. Each tonne is 1000 kg, so you need 1000 times as many kilograms as tonnes. The kilogram is the smaller unit, so the number gets bigger: multiply by 1000.
   0.02 × 1000 = 20 kg
3. Change kilograms to grams. Use the fact 1 kg = 1000 g. Each kilogram is 1000 g, so you need 1000 times as many grams as kilograms. The gram is the smaller unit, so the number gets bigger: multiply by 1000.
   20 × 1000 = 20,000 g
4. Write the answer with its unit. We went one unit at a time so each step uses a fact you already know.
   0.02 tonnes = 20,000 g

Check. Convert back: 20,000 g gives 0.02 tonnes (20,000 ÷ 1,000,000 = 0.02). ✓

Watch out. Ask yourself: will the number get bigger or smaller? Metres to centimetres: you get more of the smaller unit, so the number grows.

Key words. A unit is a standard size we measure in. Kilometres and millimetres measure the same kind of thing, but one is bigger than the other.

Method. To change units, use the fact that links them. Changing to a smaller unit means a bigger number (multiply); changing to a bigger unit means a smaller number (divide).

1. Decide what should happen to the number: kilometres to millimetres. Kilometres are the bigger unit and millimetres are the smaller unit, so it takes more millimetres to make the same amount. We expect the number to get bigger.
   3 km → ? mm
2. Change kilometres to metres. Use the fact 1 km = 1000 m. Each kilometre is 1000 m, so you need 1000 times as many metres as kilometres. The metre is the smaller unit, so the number gets bigger: multiply by 1000.
   3 × 1000 = 3000 m
3. Change metres to centimetres. Use the fact 1 m = 100 cm. Each metre is 100 cm, so you need 100 times as many centimetres as metres. The centimetre is the smaller unit, so the number gets bigger: multiply by 100.
   3000 × 100 = 300,000 cm
4. Change centimetres to millimetres. Use the fact 1 cm = 10 mm. Each centimetre is 10 mm, so you need 10 times as many millimetres as centimetres. The millimetre is the smaller unit, so the number gets bigger: multiply by 10.
   300,000 × 10 = 3,000,000 mm
5. Write the answer with its unit. We went one unit at a time so each step uses a fact you already know.
   3 km = 3,000,000 mm

Check. Convert back: 3,000,000 mm gives 3 km (3,000,000 ÷ 1,000,000 = 3). ✓

Watch out. Ask yourself: will the number get bigger or smaller? Metres to centimetres: you get more of the smaller unit, so the number grows.

Key words. A unit is a standard size we measure in. Milligrams and kilograms measure the same kind of thing, but one is bigger than the other.

Method. To change units, use the fact that links them. Changing to a smaller unit means a bigger number (multiply); changing to a bigger unit means a smaller number (divide).

1. Decide what should happen to the number: milligrams to kilograms. Milligrams are the smaller unit and kilograms are the bigger unit, so it takes fewer kilograms to make the same amount. We expect the number to get smaller.
   5,000,000 mg → ? kg
2. Change milligrams to grams. Use the fact 1 g = 1000 mg. It takes 1000 milligrams to make one gram, so you need 1000 times fewer grams than milligrams. The gram is the bigger unit, so the number gets smaller: divide by 1000.
   5,000,000 ÷ 1000 = 5000 g
3. Change grams to kilograms. Use the fact 1 kg = 1000 g. It takes 1000 grams to make one kilogram, so you need 1000 times fewer kilograms than grams. The kilogram is the bigger unit, so the number gets smaller: divide by 1000.
   5000 ÷ 1000 = 5 kg
4. Write the answer with its unit. We went one unit at a time so each step uses a fact you already know.
   5,000,000 mg = 5 kg

Check. Convert back: 5 kg gives 5,000,000 mg (5 × 1,000,000 = 5,000,000). ✓

Watch out. Ask yourself: will the number get bigger or smaller? Metres to centimetres: you get more of the smaller unit, so the number grows.

Key words. A unit is a standard size we measure in. Minutes and seconds measure the same kind of thing, but one is bigger than the other.

Method. To change units, use the fact that links them. Changing to a smaller unit means a bigger number (multiply); changing to a bigger unit means a smaller number (divide).

1. Decide what should happen to the number: minutes to seconds. Minutes are the bigger unit and seconds are the smaller unit, so it takes more seconds to make the same amount. We expect the number to get bigger.
   3 minutes → ? seconds
2. Change minutes to seconds. Use the fact 1 minute = 60 seconds. Each minute is 60 seconds, so you need 60 times as many seconds as minutes. The second is the smaller unit, so the number gets bigger: multiply by 60.
   3 × 60 = 180 seconds
3. Write the answer with its unit. Always finish by writing the new unit.
   3 minutes = 180 seconds

Check. Convert back: 180 seconds gives 3 minutes (180 ÷ 60 = 3). ✓

Watch out. Ask yourself: will the number get bigger or smaller? Metres to centimetres: you get more of the smaller unit, so the number grows.

Key words. A unit is a standard size we measure in. Hours and minutes measure the same kind of thing, but one is bigger than the other.

Method. To change units, use the fact that links them. Changing to a smaller unit means a bigger number (multiply); changing to a bigger unit means a smaller number (divide).

1. Decide what should happen to the number: hours to minutes. Hours are the bigger unit and minutes are the smaller unit, so it takes more minutes to make the same amount. We expect the number to get bigger.
   2 hours → ? minutes
2. Change hours to minutes. Use the fact 1 hour = 60 minutes. Each hour is 60 minutes, so you need 60 times as many minutes as hours. The minute is the smaller unit, so the number gets bigger: multiply by 60.
   2 × 60 = 120 minutes
3. Write the answer with its unit. Always finish by writing the new unit.
   2 hours = 120 minutes

Check. Convert back: 120 minutes gives 2 hours (120 ÷ 60 = 2). ✓

Watch out. Ask yourself: will the number get bigger or smaller? Metres to centimetres: you get more of the smaller unit, so the number grows.

Key words. A unit is a standard size we measure in. Seconds and minutes measure the same kind of thing, but one is bigger than the other.

Method. To change units, use the fact that links them. Changing to a smaller unit means a bigger number (multiply); changing to a bigger unit means a smaller number (divide).

1. Decide what should happen to the number: seconds to minutes. Seconds are the smaller unit and minutes are the bigger unit, so it takes fewer minutes to make the same amount. We expect the number to get smaller.
   180 seconds → ? minutes
2. Change seconds to minutes. Use the fact 1 minute = 60 seconds. It takes 60 seconds to make one minute, so you need 60 times fewer minutes than seconds. The minute is the bigger unit, so the number gets smaller: divide by 60.
   180 ÷ 60 = 3 minutes
3. Write the answer with its unit. Always finish by writing the new unit.
   180 seconds = 3 minutes

Check. Convert back: 3 minutes gives 180 seconds (3 × 60 = 180). ✓

Watch out. Ask yourself: will the number get bigger or smaller? Metres to centimetres: you get more of the smaller unit, so the number grows.

Key words. A unit is a standard size we measure in. Minutes and hours measure the same kind of thing, but one is bigger than the other.

Method. To change units, use the fact that links them. Changing to a smaller unit means a bigger number (multiply); changing to a bigger unit means a smaller number (divide).

1. Decide what should happen to the number: minutes to hours. Minutes are the smaller unit and hours are the bigger unit, so it takes fewer hours to make the same amount. We expect the number to get smaller.
   300 minutes → ? hours
2. Change minutes to hours. Use the fact 1 hour = 60 minutes. It takes 60 minutes to make one hour, so you need 60 times fewer hours than minutes. The hour is the bigger unit, so the number gets smaller: divide by 60.
   300 ÷ 60 = 5 hours
3. Write the answer with its unit. Always finish by writing the new unit.
   300 minutes = 5 hours

Check. Convert back: 5 hours gives 300 minutes (5 × 60 = 300). ✓

Watch out. Ask yourself: will the number get bigger or smaller? Metres to centimetres: you get more of the smaller unit, so the number grows.

Key words. A unit is a standard size we measure in. Days and hours measure the same kind of thing, but one is bigger than the other.

Method. To change units, use the fact that links them. Changing to a smaller unit means a bigger number (multiply); changing to a bigger unit means a smaller number (divide).

1. Decide what should happen to the number: days to hours. Days are the bigger unit and hours are the smaller unit, so it takes more hours to make the same amount. We expect the number to get bigger.
   5 days → ? hours
2. Change days to hours. Use the fact 1 day = 24 hours. Each day is 24 hours, so you need 24 times as many hours as days. The hour is the smaller unit, so the number gets bigger: multiply by 24.
   5 × 24 = 120 hours
3. Write the answer with its unit. Always finish by writing the new unit.
   5 days = 120 hours

Check. Convert back: 120 hours gives 5 days (120 ÷ 24 = 5). ✓

Watch out. Ask yourself: will the number get bigger or smaller? Metres to centimetres: you get more of the smaller unit, so the number grows.

Key words. A unit is a standard size we measure in. Weeks and days measure the same kind of thing, but one is bigger than the other.

Method. To change units, use the fact that links them. Changing to a smaller unit means a bigger number (multiply); changing to a bigger unit means a smaller number (divide).

1. Decide what should happen to the number: weeks to days. Weeks are the bigger unit and days are the smaller unit, so it takes more days to make the same amount. We expect the number to get bigger.
   3 weeks → ? days
2. Change weeks to days. Use the fact 1 week = 7 days. Each week is 7 days, so you need 7 times as many days as weeks. The day is the smaller unit, so the number gets bigger: multiply by 7.
   3 × 7 = 21 days
3. Write the answer with its unit. Always finish by writing the new unit.
   3 weeks = 21 days

Check. Convert back: 21 days gives 3 weeks (21 ÷ 7 = 3). ✓

Watch out. Ask yourself: will the number get bigger or smaller? Metres to centimetres: you get more of the smaller unit, so the number grows.

Method. Convert from the 12-hour clock to the 24-hour clock: add 12 to pm hours (except 12 pm); 12 am becomes 00.

1. Decide: is it am or pm? am is before midday and pm is after midday. This decides whether we add 12.
   7:30 am
2. Keep the hour (am). Morning hours are the same on both clocks.
   The hour stays 7
3. Write it with four digits. Always use two digits for the hour and two for the minutes.
   07:30

Check. 07:30 converted back is 7:30 am. ✓

Method. Convert from the 12-hour clock to the 24-hour clock: add 12 to pm hours (except 12 pm); 12 am becomes 00.

1. Decide: is it am or pm? am is before midday and pm is after midday. This decides whether we add 12.
   2:15 pm
2. Add 12 to the hour (pm). The 24-hour clock carries on counting after 12 at midday: 1 pm is 13:00.
   2 + 12 = 14
3. Write it with four digits. Always use two digits for the hour and two for the minutes.
   14:15

Check. 14:15 converted back is 2:15 pm. ✓

Method. Convert from the 12-hour clock to the 24-hour clock: add 12 to pm hours (except 12 pm); 12 am becomes 00.

1. Decide: is it am or pm? am is before midday and pm is after midday. This decides whether we add 12.
   11:40 pm
2. Add 12 to the hour (pm). The 24-hour clock carries on counting after 12 at midday: 1 pm is 13:00.
   11 + 12 = 23
3. Write it with four digits. Always use two digits for the hour and two for the minutes.
   23:40

Check. 23:40 converted back is 11:40 pm. ✓

Method. Convert from the 12-hour clock to the 24-hour clock: add 12 to pm hours (except 12 pm); 12 am becomes 00.

1. Decide: is it am or pm? am is before midday and pm is after midday. This decides whether we add 12.
   12:05 am
2. Keep the hour (am). Morning hours are the same on both clocks. The only change is that 12 am (midnight) becomes 00.
   12 am becomes 00
3. Write it with four digits. Always use two digits for the hour and two for the minutes.
   00:05

Check. 00:05 converted back is 12:05 am. ✓

Method. Convert from the 12-hour clock to the 24-hour clock: add 12 to pm hours (except 12 pm); 12 am becomes 00.

1. Decide: is it am or pm? am is before midday and pm is after midday. This decides whether we add 12.
   12:30 pm
2. Keep the hour: 12 pm is midday. 12:00 to 12:59 pm are the same on both clocks.
   The hour stays 12
3. Write it with four digits. Always use two digits for the hour and two for the minutes.
   12:30

Check. 12:30 converted back is 12:30 pm. ✓

Method. Convert from the 12-hour clock to the 24-hour clock: add 12 to pm hours (except 12 pm); 12 am becomes 00.

1. Decide: is it am or pm? am is before midday and pm is after midday. This decides whether we add 12.
   9:05 pm
2. Add 12 to the hour (pm). The 24-hour clock carries on counting after 12 at midday: 1 pm is 13:00.
   9 + 12 = 21
3. Write it with four digits. Always use two digits for the hour and two for the minutes.
   21:05

Check. 21:05 converted back is 9:05 pm. ✓

Method. Convert from the 24-hour clock to the 12-hour clock: subtract 12 from hours bigger than 12 and write pm.

1. Look at the hour. Before 12:00 the time is in the morning (am) and the hour stays the same.
   06:45
2. Write it on the 12-hour clock. Add am.
   6:45 am

Check. Convert back: 6:45 am on a 24-hour clock is 06:45. ✓

Method. Convert from the 24-hour clock to the 12-hour clock: subtract 12 from hours bigger than 12 and write pm.

1. Subtract 12 from the hour. After 12:59 the time is pm. This undoes the “add 12” rule.
   13 − 12 = 1
2. Write it with pm. The minutes do not change.
   1:20 pm

Check. Convert back: 1:20 pm on a 24-hour clock is 13:20. ✓

Method. Convert from the 24-hour clock to the 12-hour clock: subtract 12 from hours bigger than 12 and write pm.

1. Subtract 12 from the hour. After 12:59 the time is pm. This undoes the “add 12” rule.
   20 − 12 = 8
2. Write it with pm. The minutes do not change.
   8:05 pm

Check. Convert back: 8:05 pm on a 24-hour clock is 20:05. ✓

Method. Convert from the 24-hour clock to the 12-hour clock: subtract 12 from hours bigger than 12 and write pm.

1. Look at the hour. 00 hours means just after midnight.
   00:15
2. Write it on the 12-hour clock. Midnight is called 12 am.
   12:15 am

Check. Convert back: 12:15 am on a 24-hour clock is 00:15. ✓

Method. Convert from the 24-hour clock to the 12-hour clock: subtract 12 from hours bigger than 12 and write pm.

1. Look at the hour. 12:00 to 12:59 is just after midday (pm) and the hour stays 12.
   12:50
2. Write it on the 12-hour clock. Add pm.
   12:50 pm

Check. Convert back: 12:50 pm on a 24-hour clock is 12:50. ✓

Method. Convert from the 24-hour clock to the 12-hour clock: subtract 12 from hours bigger than 12 and write pm.

1. Subtract 12 from the hour. After 12:59 the time is pm. This undoes the “add 12” rule.
   23 − 12 = 11
2. Write it with pm. The minutes do not change.
   11:59 pm

Check. Convert back: 11:59 pm on a 24-hour clock is 23:59. ✓

Key words. The 24-hour clock counts the hours from 00:00 to 23:59. 15:30 is 3:30 pm. Duration means how long something lasts.

Method. To find a time difference, count on from the start time to the finish time in easy jumps: to the next whole hour, then whole hours, then the minutes left.

1. Write both times on the 24-hour clock. The 24-hour clock avoids am and pm mix-ups.
   Start 07:15, finish 09:40
2. Count on to the next whole hour. Counting on in easy jumps is safer than subtracting 24-hour times, because there are 60 minutes (not 100) in an hour.
   07:15 to 08:00 = 45 minutes
3. Count on in whole hours. Now we are at the start of an hour, so we can jump whole hours.
   08:00 to 09:00 = 1 hours
4. Count on the remaining minutes. Finish by counting on to the finishing time.
   09:00 to 09:40 = 40 minutes
5. Add the pieces together. The total is the time taken.
   45 minutes + 1 hour + 40 minutes = 2 hours 25 minutes

Check. Add back: 07:15 + 2 hours 25 minutes = 09:40. ✓

Watch out. Never subtract 24-hour times like 1420 − 0950 as ordinary numbers. An hour has 60 minutes, not 100.

Key words. The 24-hour clock counts the hours from 00:00 to 23:59. 15:30 is 3:30 pm. Duration means how long something lasts.

Method. To find a time difference, count on from the start time to the finish time in easy jumps: to the next whole hour, then whole hours, then the minutes left.

1. Write both times on the 24-hour clock. The 24-hour clock avoids am and pm mix-ups.
   Start 10:50, finish 14:25
2. Count on to the next whole hour. Counting on in easy jumps is safer than subtracting 24-hour times, because there are 60 minutes (not 100) in an hour.
   10:50 to 11:00 = 10 minutes
3. Count on in whole hours. Now we are at the start of an hour, so we can jump whole hours.
   11:00 to 14:00 = 3 hours
4. Count on the remaining minutes. Finish by counting on to the finishing time.
   14:00 to 14:25 = 25 minutes
5. Add the pieces together. The total is the time taken.
   10 minutes + 3 hours + 25 minutes = 3 hours 35 minutes

Check. Add back: 10:50 + 3 hours 35 minutes = 14:25. ✓

Watch out. Never subtract 24-hour times like 1420 − 0950 as ordinary numbers. An hour has 60 minutes, not 100.

Key words. The 24-hour clock counts the hours from 00:00 to 23:59. 15:30 is 3:30 pm. Duration means how long something lasts.

Method. To find a time difference, count on from the start time to the finish time in easy jumps: to the next whole hour, then whole hours, then the minutes left.

1. Write both times on the 24-hour clock. The 24-hour clock avoids am and pm mix-ups.
   Start 16:35, finish 20:10
2. Count on to the next whole hour. Counting on in easy jumps is safer than subtracting 24-hour times, because there are 60 minutes (not 100) in an hour.
   16:35 to 17:00 = 25 minutes
3. Count on in whole hours. Now we are at the start of an hour, so we can jump whole hours.
   17:00 to 20:00 = 3 hours
4. Count on the remaining minutes. Finish by counting on to the finishing time.
   20:00 to 20:10 = 10 minutes
5. Add the pieces together. The total is the time taken.
   25 minutes + 3 hours + 10 minutes = 3 hours 35 minutes

Check. Add back: 16:35 + 3 hours 35 minutes = 20:10. ✓

Watch out. Never subtract 24-hour times like 1420 − 0950 as ordinary numbers. An hour has 60 minutes, not 100.

Key words. The 24-hour clock counts the hours from 00:00 to 23:59. 15:30 is 3:30 pm. Duration means how long something lasts.

Method. To find a time difference, count on from the start time to the finish time in easy jumps: to the next whole hour, then whole hours, then the minutes left.

1. Write both times on the 24-hour clock. The 24-hour clock avoids am and pm mix-ups.
   Start 22:20, finish 01:05 (the next day)
2. Count on to the next whole hour. Counting on in easy jumps is safer than subtracting 24-hour times, because there are 60 minutes (not 100) in an hour.
   22:20 to 23:00 = 40 minutes
3. Count on in whole hours. Now we are at the start of an hour, so we can jump whole hours.
   23:00 to 01:00 = 2 hours
4. Count on the remaining minutes. Finish by counting on to the finishing time.
   01:00 to 01:05 = 5 minutes
5. Add the pieces together. The total is the time taken.
   40 minutes + 2 hours + 5 minutes = 2 hours 45 minutes

Check. Add back: 22:20 + 2 hours 45 minutes = 01:05. ✓

Watch out. Never subtract 24-hour times like 1420 − 0950 as ordinary numbers. An hour has 60 minutes, not 100.

Method. Add the hours, then the minutes. Carry an hour when the minutes pass 60.

1. Add the hours first. Whole hours do not change the minutes part of the time.
   08:30 + 2 hours = 10:30
2. Add the minutes. If the minutes go past 60, carry 1 hour. Think "how many minutes to the next hour?"
   10:30 + 45 minutes = 11:15
3. Write the answer. Give the time on the 24-hour clock.
   11:15

Check. Count back: 11:15 minus 2 hours 45 minutes = 08:30. ✓

Method. Add the hours, then the minutes. Carry an hour when the minutes pass 60.

1. Add the hours first. Whole hours do not change the minutes part of the time.
   13:40 + 1 hour = 14:40
2. Add the minutes. If the minutes go past 60, carry 1 hour. Think "how many minutes to the next hour?"
   14:40 + 35 minutes = 15:15
3. Write the answer. Give the time on the 24-hour clock.
   15:15

Check. Count back: 15:15 minus 1 hour 35 minutes = 13:40. ✓

Method. Add the hours, then the minutes. Carry an hour when the minutes pass 60.

1. Add the hours first. Whole hours do not change the minutes part of the time.
   18:20 + 3 hours = 21:20
2. Add the minutes. If the minutes go past 60, carry 1 hour. Think "how many minutes to the next hour?"
   21:20 + 50 minutes = 22:10
3. Write the answer. Give the time on the 24-hour clock.
   22:10

Check. Count back: 22:10 minus 3 hours 50 minutes = 18:20. ✓

Method. Add the hours, then the minutes. Carry an hour when the minutes pass 60.

1. Add the hours first. Whole hours do not change the minutes part of the time.
   21:45 + 4 hours = 01:45
2. Add the minutes. If the minutes go past 60, carry 1 hour. Think "how many minutes to the next hour?"
   01:45 + 30 minutes = 02:15
3. Write the answer (it is the next day). The time has passed 24:00, so it is after midnight on the next day.
   02:15 the next day

Check. Count back: 02:15 minus 4 hours 30 minutes = 21:45. ✓

Method. Decimal hours are not hours and minutes. Keep the whole hours and multiply the decimal part by 60 to get minutes.

1. Split off the whole hours. The digits before the decimal point are whole hours.
   3.5 hours = 3 hours + 0.5 hours
2. Change the decimal part to minutes. There are 60 minutes in 1 hour, so multiply the decimal by 60.
   0.5 × 60 = 30 minutes
3. Put them together.
   3 hours 30 minutes

Check. 30 ÷ 60 = 0.5, so 3 hours 30 minutes is 3.5 hours. ✓

Watch out. 2.5 hours is not 2 hours 50 minutes. The .5 is half an hour = 30 minutes.

Method. Decimal hours are not hours and minutes. Keep the whole hours and multiply the decimal part by 60 to get minutes.

1. Split off the whole hours. The digits before the decimal point are whole hours.
   1.25 hours = 1 hours + 0.25 hours
2. Change the decimal part to minutes. There are 60 minutes in 1 hour, so multiply the decimal by 60.
   0.25 × 60 = 15 minutes
3. Put them together.
   1 hours 15 minutes

Check. 15 ÷ 60 = 0.25, so 1 hours 15 minutes is 1.25 hours. ✓

Watch out. 2.5 hours is not 2 hours 50 minutes. The .5 is half an hour = 30 minutes.

Method. Decimal hours are not hours and minutes. Keep the whole hours and multiply the decimal part by 60 to get minutes.

1. Split off the whole hours. The digits before the decimal point are whole hours.
   2.4 hours = 2 hours + 0.4 hours
2. Change the decimal part to minutes. There are 60 minutes in 1 hour, so multiply the decimal by 60.
   0.4 × 60 = 24 minutes
3. Put them together.
   2 hours 24 minutes

Check. 24 ÷ 60 = 0.4, so 2 hours 24 minutes is 2.4 hours. ✓

Watch out. 2.5 hours is not 2 hours 50 minutes. The .5 is half an hour = 30 minutes.

Method. Decimal hours are not hours and minutes. Keep the whole hours and multiply the decimal part by 60 to get minutes.

1. Split off the whole hours. The digits before the decimal point are whole hours.
   0.75 hours = 0 hours + 0.75 hours
2. Change the decimal part to minutes. There are 60 minutes in 1 hour, so multiply the decimal by 60.
   0.75 × 60 = 45 minutes
3. Put them together.
   0 hours 45 minutes

Check. 45 ÷ 60 = 0.75, so 0 hours 45 minutes is 0.75 hours. ✓

Watch out. 2.5 hours is not 2 hours 50 minutes. The .5 is half an hour = 30 minutes.

Method. To write hours and minutes as decimal hours, divide the minutes by 60 and add the whole hours.

1. Change the minutes to a fraction of an hour. There are 60 minutes in 1 hour, so divide the minutes by 60.
   30 ÷ 60 = 0.5
2. Add the whole hours.
   2 + 0.5 = 2.5 hours

Check. 0.5 × 60 = 30 minutes. ✓

Watch out. Divide the minutes by 60, not by 100.

Method. To write hours and minutes as decimal hours, divide the minutes by 60 and add the whole hours.

1. Change the minutes to a fraction of an hour. There are 60 minutes in 1 hour, so divide the minutes by 60.
   45 ÷ 60 = 0.75
2. Add the whole hours.
   1 + 0.75 = 1.75 hours

Check. 0.75 × 60 = 45 minutes. ✓

Watch out. Divide the minutes by 60, not by 100.

Method. To write hours and minutes as decimal hours, divide the minutes by 60 and add the whole hours.

1. Change the minutes to a fraction of an hour. There are 60 minutes in 1 hour, so divide the minutes by 60.
   12 ÷ 60 = 0.2
2. Add the whole hours.
   3 + 0.2 = 3.2 hours

Check. 0.2 × 60 = 12 minutes. ✓

Watch out. Divide the minutes by 60, not by 100.

Method. To write hours and minutes as decimal hours, divide the minutes by 60 and add the whole hours.

1. Change the minutes to a fraction of an hour. There are 60 minutes in 1 hour, so divide the minutes by 60.
   6 ÷ 60 = 0.1
2. Add the whole hours.
   4 + 0.1 = 4.1 hours

Check. 0.1 × 60 = 6 minutes. ✓

Watch out. Divide the minutes by 60, not by 100.

Key words. The 24-hour clock counts the hours from 00:00 to 23:59. 15:30 is 3:30 pm. Duration means how long something lasts.

Method. To find a time difference, count on from the start time to the finish time in easy jumps: to the next whole hour, then whole hours, then the minutes left.

1. Write both times on the 24-hour clock. The 24-hour clock avoids am and pm mix-ups.
   Start 07:48, finish 09:41
2. Count on to the next whole hour. Counting on in easy jumps is safer than subtracting 24-hour times, because there are 60 minutes (not 100) in an hour.
   07:48 to 08:00 = 12 minutes
3. Count on in whole hours. Now we are at the start of an hour, so we can jump whole hours.
   08:00 to 09:00 = 1 hours
4. Count on the remaining minutes. Finish by counting on to the finishing time.
   09:00 to 09:41 = 41 minutes
5. Add the pieces together. The total is the time taken.
   12 minutes + 1 hour + 41 minutes = 1 hour 53 minutes

Check. Add back: 07:48 + 1 hour 53 minutes = 09:41. ✓

Watch out. Never subtract 24-hour times like 1420 − 0950 as ordinary numbers. An hour has 60 minutes, not 100.

Key words. The 24-hour clock counts the hours from 00:00 to 23:59. 15:30 is 3:30 pm. Duration means how long something lasts.

Method. To find a time difference, count on from the start time to the finish time in easy jumps: to the next whole hour, then whole hours, then the minutes left.

1. Write both times on the 24-hour clock. The 24-hour clock avoids am and pm mix-ups.
   Start 08:26, finish 09:05
2. Count on to the next whole hour. Counting on in easy jumps is safer than subtracting 24-hour times, because there are 60 minutes (not 100) in an hour.
   08:26 to 09:00 = 34 minutes
3. Count on the remaining minutes. Finish by counting on to the finishing time.
   09:00 to 09:05 = 5 minutes
4. Add the pieces together. The total is the time taken.
   34 minutes + 5 minutes = 39 minutes

Check. Add back: 08:26 + 39 minutes = 09:05. ✓

Watch out. Never subtract 24-hour times like 1420 − 0950 as ordinary numbers. An hour has 60 minutes, not 100.

Method. Use the count-on method twice.

1. Bellview to Corton. Count on from 07:48 to 08:00 (12 min), then to 08:26 (26 min).
   12 + 26 = 38 minutes
2. Corton to Eastgate. Count on from 08:26 to 09:00 (34 min), then to 09:41 (41 min).
   34 + 41 = 75 minutes = 1 hour 15 minutes

Check. 38 + 75 = 113 minutes = 1 hour 53 minutes, the same as Bellview to Eastgate (07:48 to 09:41). ✓

Key words. Area is the amount of flat surface, measured in square units such as cm². Volume is the space inside a 3D shape, measured in cubic units such as cm³.

Method. To change area units, square (or cube) the length factor. The area factor is the length factor squared.

1. Write the length fact for the two units. Area and volume units are built from lengths, so start with the length fact.
   1 m = 100 cm
2. Find how many cm² fit in 1 m². A square of side 1 m has side 100 cm. Its area is the length squared. The number of small squares is length × length.
   1 m² = 100 cm × 100 cm = 10,000 cm²
3. Multiply by the area/volume factor. We are changing to the smaller unit, so the number of cm² is bigger.
   2 × 10,000 = 20,000 cm²

Check. Convert back: 20,000 cm² ÷ 10,000 = 2 m². ✓

Watch out. Do not use the length factor on its own. 1 m = 100 cm but 1 m² is not 100 cm²; it is 10,000 cm².

Key words. Area is the amount of flat surface, measured in square units such as cm². Volume is the space inside a 3D shape, measured in cubic units such as cm³.

Method. To change area units, square (or cube) the length factor. The area factor is the length factor squared.

1. Write the length fact for the two units. Area and volume units are built from lengths, so start with the length fact.
   1 m = 100 cm
2. Find how many cm² fit in 1 m². A square of side 1 m has side 100 cm. Its area is the length squared. The number of small squares is length × length.
   1 m² = 100 cm × 100 cm = 10,000 cm²
3. Multiply by the area/volume factor. We are changing to the smaller unit, so the number of cm² is bigger.
   0.5 × 10,000 = 5000 cm²

Check. Convert back: 5000 cm² ÷ 10,000 = 0.5 m². ✓

Watch out. Do not use the length factor on its own. 1 m = 100 cm but 1 m² is not 100 cm²; it is 10,000 cm².

Key words. Area is the amount of flat surface, measured in square units such as cm². Volume is the space inside a 3D shape, measured in cubic units such as cm³.

Method. To change area units, square (or cube) the length factor. The area factor is the length factor squared.

1. Write the length fact for the two units. Area and volume units are built from lengths, so start with the length fact.
   1 cm = 10 mm
2. Find how many mm² fit in 1 cm². A square of side 1 cm has side 10 mm. Its area is the length squared. The number of small squares is length × length.
   1 cm² = 10 mm × 10 mm = 100 mm²
3. Multiply by the area/volume factor. We are changing to the smaller unit, so the number of mm² is bigger.
   3 × 100 = 300 mm²

Check. Convert back: 300 mm² ÷ 100 = 3 cm². ✓

Watch out. Use the square of the length factor, not the length factor itself.

Key words. Area is the amount of flat surface, measured in square units such as cm². Volume is the space inside a 3D shape, measured in cubic units such as cm³.

Method. To change area units, square (or cube) the length factor. The area factor is the length factor squared.

1. Write the length fact for the two units. Area and volume units are built from lengths, so start with the length fact.
   1 cm = 10 mm
2. Find how many mm² fit in 1 cm². A square of side 1 cm has side 10 mm. Its area is the length squared. The number of small squares is length × length.
   1 cm² = 10 mm × 10 mm = 100 mm²
3. Multiply by the area/volume factor. We are changing to the smaller unit, so the number of mm² is bigger.
   1.2 × 100 = 120 mm²

Check. Convert back: 120 mm² ÷ 100 = 1.2 cm². ✓

Watch out. Use the square of the length factor, not the length factor itself.

Key words. Area is the amount of flat surface, measured in square units such as cm². Volume is the space inside a 3D shape, measured in cubic units such as cm³.

Method. To change area units, square (or cube) the length factor. The area factor is the length factor squared.

1. Write the length fact for the two units. Area and volume units are built from lengths, so start with the length fact.
   1 m = 100 cm
2. Find how many cm² fit in 1 m². A square of side 1 m has side 100 cm. Its area is the length squared. The number of small squares is length × length.
   1 m² = 100 cm × 100 cm = 10,000 cm²
3. Divide by the area/volume factor. We are changing to the bigger unit, so the number of m² is smaller.
   50,000 ÷ 10,000 = 5 m²

Check. Convert back: 5 m² × 10,000 = 50,000 cm². ✓

Watch out. Do not use the length factor on its own. 1 m = 100 cm but 1 m² is not 100 cm²; it is 10,000 cm².

Key words. Area is the amount of flat surface, measured in square units such as cm². Volume is the space inside a 3D shape, measured in cubic units such as cm³.

Method. To change area units, square (or cube) the length factor. The area factor is the length factor squared.

1. Write the length fact for the two units. Area and volume units are built from lengths, so start with the length fact.
   1 m = 100 cm
2. Find how many cm² fit in 1 m². A square of side 1 m has side 100 cm. Its area is the length squared. The number of small squares is length × length.
   1 m² = 100 cm × 100 cm = 10,000 cm²
3. Divide by the area/volume factor. We are changing to the bigger unit, so the number of m² is smaller.
   25,000 ÷ 10,000 = 2.5 m²

Check. Convert back: 2.5 m² × 10,000 = 25,000 cm². ✓

Watch out. Do not use the length factor on its own. 1 m = 100 cm but 1 m² is not 100 cm²; it is 10,000 cm².

Key words. Area is the amount of flat surface, measured in square units such as cm². Volume is the space inside a 3D shape, measured in cubic units such as cm³.

Method. To change area units, square (or cube) the length factor. The area factor is the length factor squared.

1. Write the length fact for the two units. Area and volume units are built from lengths, so start with the length fact.
   1 cm = 10 mm
2. Find how many mm² fit in 1 cm². A square of side 1 cm has side 10 mm. Its area is the length squared. The number of small squares is length × length.
   1 cm² = 10 mm × 10 mm = 100 mm²
3. Divide by the area/volume factor. We are changing to the bigger unit, so the number of cm² is smaller.
   700 ÷ 100 = 7 cm²

Check. Convert back: 7 cm² × 100 = 700 mm². ✓

Watch out. Use the square of the length factor, not the length factor itself.

Key words. Area is the amount of flat surface, measured in square units such as cm². Volume is the space inside a 3D shape, measured in cubic units such as cm³.

Method. To change area units, square (or cube) the length factor. The area factor is the length factor squared.

1. Write the length fact for the two units. Area and volume units are built from lengths, so start with the length fact.
   1 cm = 10 mm
2. Find how many mm² fit in 1 cm². A square of side 1 cm has side 10 mm. Its area is the length squared. The number of small squares is length × length.
   1 cm² = 10 mm × 10 mm = 100 mm²
3. Divide by the area/volume factor. We are changing to the bigger unit, so the number of cm² is smaller.
   450 ÷ 100 = 4.5 cm²

Check. Convert back: 4.5 cm² × 100 = 450 mm². ✓

Watch out. Use the square of the length factor, not the length factor itself.

Key words. Area is the amount of flat surface, measured in square units such as cm². Volume is the space inside a 3D shape, measured in cubic units such as cm³.

Method. To change area units, square (or cube) the length factor. The area factor is the length factor squared.

1. Write the length fact for the two units. Area and volume units are built from lengths, so start with the length fact.
   1 km = 1000 m
2. Find how many m² fit in 1 km². A square of side 1 km has side 1000 m. Its area is the length squared. The number of small squares is length × length.
   1 km² = 1000 m × 1000 m = 1,000,000 m²
3. Multiply by the area/volume factor. We are changing to the smaller unit, so the number of m² is bigger.
   2 × 1,000,000 = 2,000,000 m²

Check. Convert back: 2,000,000 m² ÷ 1,000,000 = 2 km². ✓

Watch out. Use the square of the length factor, not the length factor itself.

Key words. Area is the amount of flat surface, measured in square units such as cm². Volume is the space inside a 3D shape, measured in cubic units such as cm³.

Method. To change area units, square (or cube) the length factor. The area factor is the length factor squared.

1. Write the length fact for the two units. Area and volume units are built from lengths, so start with the length fact.
   1 km = 1000 m
2. Find how many m² fit in 1 km². A square of side 1 km has side 1000 m. Its area is the length squared. The number of small squares is length × length.
   1 km² = 1000 m × 1000 m = 1,000,000 m²
3. Divide by the area/volume factor. We are changing to the bigger unit, so the number of km² is smaller.
   3,500,000 ÷ 1,000,000 = 3.5 km²

Check. Convert back: 3.5 km² × 1,000,000 = 3,500,000 m². ✓

Watch out. Use the square of the length factor, not the length factor itself.

Key words. Area is the amount of flat surface, measured in square units such as cm². Volume is the space inside a 3D shape, measured in cubic units such as cm³.

Method. To change area units, square (or cube) the length factor. The area factor is the length factor squared.

1. Write the length fact for the two units. Area and volume units are built from lengths, so start with the length fact.
   1 m = 100 cm
2. Find how many cm² fit in 1 m². A square of side 1 m has side 100 cm. Its area is the length squared. The number of small squares is length × length.
   1 m² = 100 cm × 100 cm = 10,000 cm²
3. Multiply by the area/volume factor. We are changing to the smaller unit, so the number of cm² is bigger.
   0.04 × 10,000 = 400 cm²

Check. Convert back: 400 cm² ÷ 10,000 = 0.04 m². ✓

Watch out. Do not use the length factor on its own. 1 m = 100 cm but 1 m² is not 100 cm²; it is 10,000 cm².

Key words. Area is the amount of flat surface, measured in square units such as cm². Volume is the space inside a 3D shape, measured in cubic units such as cm³.

Method. To change area units, square (or cube) the length factor. The area factor is the length factor squared.

1. Write the length fact for the two units. Area and volume units are built from lengths, so start with the length fact.
   1 m = 100 cm
2. Find how many cm² fit in 1 m². A square of side 1 m has side 100 cm. Its area is the length squared. The number of small squares is length × length.
   1 m² = 100 cm × 100 cm = 10,000 cm²
3. Divide by the area/volume factor. We are changing to the bigger unit, so the number of m² is smaller.
   62,000 ÷ 10,000 = 6.2 m²

Check. Convert back: 6.2 m² × 10,000 = 62,000 cm². ✓

Watch out. Do not use the length factor on its own. 1 m = 100 cm but 1 m² is not 100 cm²; it is 10,000 cm².

Key words. Area is the amount of flat surface, measured in square units such as cm². Volume is the space inside a 3D shape, measured in cubic units such as cm³.

Method. To change volume units, square (or cube) the length factor. The volume factor is the length factor cubed.

1. Write the length fact for the two units. Area and volume units are built from lengths, so start with the length fact.
   1 m = 100 cm
2. Find how many cm³ fit in 1 m³. A cube of side 1 m has side 100 cm. Its volume is the length cubed. The number of small cubes is length × length × length.
   1 m³ = 100 cm × 100 cm × 100 cm = 1,000,000 cm³
3. Multiply by the area/volume factor. We are changing to the smaller unit, so the number of cm³ is bigger.
   3 × 1,000,000 = 3,000,000 cm³

Check. Convert back: 3,000,000 cm³ ÷ 1,000,000 = 3 m³. ✓

Watch out. Do not use the length factor on its own. 1 m = 100 cm but 1 m² is not 100 cm²; it is 1,000,000 cm³.

Key words. Area is the amount of flat surface, measured in square units such as cm². Volume is the space inside a 3D shape, measured in cubic units such as cm³.

Method. To change volume units, square (or cube) the length factor. The volume factor is the length factor cubed.

1. Write the length fact for the two units. Area and volume units are built from lengths, so start with the length fact.
   1 cm = 10 mm
2. Find how many mm³ fit in 1 cm³. A cube of side 1 cm has side 10 mm. Its volume is the length cubed. The number of small cubes is length × length × length.
   1 cm³ = 10 mm × 10 mm × 10 mm = 1000 mm³
3. Multiply by the area/volume factor. We are changing to the smaller unit, so the number of mm³ is bigger.
   2.5 × 1000 = 2500 mm³

Check. Convert back: 2500 mm³ ÷ 1000 = 2.5 cm³. ✓

Watch out. Use the cube of the length factor, not the length factor itself.

Key words. Area is the amount of flat surface, measured in square units such as cm². Volume is the space inside a 3D shape, measured in cubic units such as cm³.

Method. To change volume units, square (or cube) the length factor. The volume factor is the length factor cubed.

1. Write the length fact for the two units. Area and volume units are built from lengths, so start with the length fact.
   1 m = 100 cm
2. Find how many cm³ fit in 1 m³. A cube of side 1 m has side 100 cm. Its volume is the length cubed. The number of small cubes is length × length × length.
   1 m³ = 100 cm × 100 cm × 100 cm = 1,000,000 cm³
3. Divide by the area/volume factor. We are changing to the bigger unit, so the number of m³ is smaller.
   4,500,000 ÷ 1,000,000 = 4.5 m³

Check. Convert back: 4.5 m³ × 1,000,000 = 4,500,000 cm³. ✓

Watch out. Do not use the length factor on its own. 1 m = 100 cm but 1 m² is not 100 cm²; it is 1,000,000 cm³.

Key words. Area is the amount of flat surface, measured in square units such as cm². Volume is the space inside a 3D shape, measured in cubic units such as cm³.

Method. To change volume units, square (or cube) the length factor. The volume factor is the length factor cubed.

1. Write the length fact for the two units. Area and volume units are built from lengths, so start with the length fact.
   1 cm = 10 mm
2. Find how many mm³ fit in 1 cm³. A cube of side 1 cm has side 10 mm. Its volume is the length cubed. The number of small cubes is length × length × length.
   1 cm³ = 10 mm × 10 mm × 10 mm = 1000 mm³
3. Divide by the area/volume factor. We are changing to the bigger unit, so the number of cm³ is smaller.
   6000 ÷ 1000 = 6 cm³

Check. Convert back: 6 cm³ × 1000 = 6000 mm³. ✓

Watch out. Use the cube of the length factor, not the length factor itself.

Method. Volume and capacity are linked by a fact you must know. Use it to multiply or divide.

1. Write the link between the units. Capacity (litres, ml) measures liquids; volume (cm³, m³) measures space. They are two ways to measure the same amount.
   1 litre = 1000 cm³  (and 1 ml = 1 cm³)
2. Decide: multiply or divide? We are changing to the bigger unit, so we need fewer of them: divide by 1000.
   4500 ÷ 1000
3. Calculate.
   4500 ÷ 1000 = 4.5 litres

Check. Convert back: 4.5 litres × 1000 = 4500 cm³. ✓

Watch out. 1 litre is 1000 cm³ (not 100 and not 10 000). Think of a 10 cm cube: 10 × 10 × 10 = 1000 cm³ holds exactly 1 litre.

Method. Volume and capacity are linked by a fact you must know. Use it to multiply or divide.

1. Write the link between the units. Capacity (litres, ml) measures liquids; volume (cm³, m³) measures space. They are two ways to measure the same amount.
   1 litre = 1000 cm³  (and 1 ml = 1 cm³)
2. Decide: multiply or divide? There are 1000 small units in every big one, so changing to the smaller unit gives a bigger number: multiply.
   3 × 1000
3. Calculate.
   3 × 1000 = 3000 cm³

Check. Convert back: 3000 cm³ ÷ 1000 = 3 litres. ✓

Watch out. 1 litre is 1000 cm³ (not 100 and not 10 000). Think of a 10 cm cube: 10 × 10 × 10 = 1000 cm³ holds exactly 1 litre.

Method. Volume and capacity are linked by a fact you must know. Use it to multiply or divide.

1. Write the link between the units. Capacity (litres, ml) measures liquids; volume (cm³, m³) measures space. They are two ways to measure the same amount.
   1 m³ = 1000 litres  (and 1 ml = 1 cm³)
2. Decide: multiply or divide? There are 1000 small units in every big one, so changing to the smaller unit gives a bigger number: multiply.
   2 × 1000
3. Calculate.
   2 × 1000 = 2000 litres

Check. Convert back: 2000 litres ÷ 1000 = 2 m³. ✓

Watch out. 1 litre is 1000 cm³ (not 100 and not 10 000). Think of a 10 cm cube: 10 × 10 × 10 = 1000 cm³ holds exactly 1 litre.

Method. Volume and capacity are linked by a fact you must know. Use it to multiply or divide.

1. Write the link between the units. Capacity (litres, ml) measures liquids; volume (cm³, m³) measures space. They are two ways to measure the same amount.
   1 m³ = 1000 litres  (and 1 ml = 1 cm³)
2. Decide: multiply or divide? We are changing to the bigger unit, so we need fewer of them: divide by 1000.
   750 ÷ 1000
3. Calculate.
   750 ÷ 1000 = 0.75 m³

Check. Convert back: 0.75 m³ × 1000 = 750 litres. ✓

Watch out. 1 litre is 1000 cm³ (not 100 and not 10 000). Think of a 10 cm cube: 10 × 10 × 10 = 1000 cm³ holds exactly 1 litre.

Method. Find the volume in m³ and use 1 m³ = 1000 litres.

1. Volume in m³. Length × width × depth.
   25 × 10 × 1.6 = 400 m³
2. Change to litres. 1 m³ = 1000 litres, so multiply by 1000.
   400 × 1000 = 400,000 litres

Check. 400 m³ is 400 big cubes of 1 m, each holding 1000 litres. ✓

Method. Divide the volume by the rate, then change minutes to hours and minutes.

1. Divide by the rate. Time = amount ÷ rate.
   400,000 ÷ 500 = 800 minutes
2. Change to hours and minutes. 60 minutes = 1 hour.
   800 ÷ 60 = 13 remainder 20
   13 hours 20 minutes

Check. 13 × 60 + 20 = 800 minutes. ✓

Method. Use the given fact to link the two units. To change into the unit with the bigger number multiply; to change back, divide.

1. Write the conversion fact you are given. This tells us how the two units are linked. It is like an exchange rate.
   1 inch ≈ 2.5 cm
2. Decide: multiply or divide? The fact says 1 inch gives 2.5 cm, so the answer is 2.5 times the starting number: multiply by 2.5. The answer should be bigger than the number we started with.
   20 inches × 2.5
3. Calculate. Use a calculator or work it out carefully.
   20 × 2.5 = 50

Check. Work backwards: 50 ÷ 2.5 ≈ 20. ✓

Watch out. Multiplying and dividing are easy to mix up. Ask yourself: should my answer be a bigger or a smaller number than the one I started with?

Method. Use the given fact to link the two units. To change into the unit with the bigger number multiply; to change back, divide.

1. Write the conversion fact you are given. This tells us how the two units are linked. It is like an exchange rate.
   1 inch ≈ 2.5 cm
2. Decide: multiply or divide? The fact says 2.5 cm make 1 inch, so the answer is the starting number shared into groups of 2.5: divide by 2.5. The answer should be smaller than the number we started with.
   150 cm ÷ 2.5
3. Calculate. Use a calculator or work it out carefully.
   150 ÷ 2.5 = 60

Check. Work backwards: 60 × 2.5 ≈ 150. ✓

Watch out. Multiplying and dividing are easy to mix up. Ask yourself: should my answer be a bigger or a smaller number than the one I started with?

Method. Use the given fact to link the two units. To change into the unit with the bigger number multiply; to change back, divide.

1. Write the conversion fact you are given. This tells us how the two units are linked. It is like an exchange rate.
   1 mile ≈ 1.6 km
2. Decide: multiply or divide? The fact says 1 mile gives 1.6 km, so the answer is 1.6 times the starting number: multiply by 1.6. The answer should be bigger than the number we started with.
   30 miles × 1.6
3. Calculate. Use a calculator or work it out carefully.
   30 × 1.6 = 48

Check. Work backwards: 48 ÷ 1.6 ≈ 30. ✓

Watch out. Multiplying and dividing are easy to mix up. Ask yourself: should my answer be a bigger or a smaller number than the one I started with?

Method. Use the given fact to link the two units. To change into the unit with the bigger number multiply; to change back, divide.

1. Write the conversion fact you are given. This tells us how the two units are linked. It is like an exchange rate.
   1 mile ≈ 1.6 km
2. Decide: multiply or divide? The fact says 1.6 km make 1 mile, so the answer is the starting number shared into groups of 1.6: divide by 1.6. The answer should be smaller than the number we started with.
   72 km ÷ 1.6
3. Calculate. Use a calculator or work it out carefully.
   72 ÷ 1.6 = 45

Check. Work backwards: 45 × 1.6 ≈ 72. ✓

Watch out. Multiplying and dividing are easy to mix up. Ask yourself: should my answer be a bigger or a smaller number than the one I started with?

Method. Use the given fact to link the two units. To change into the unit with the bigger number multiply; to change back, divide.

1. Write the conversion fact you are given. This tells us how the two units are linked. It is like an exchange rate.
   1 kg ≈ 2.2 pounds
2. Decide: multiply or divide? The fact says 1 kilogram gives 2.2 pounds, so the answer is 2.2 times the starting number: multiply by 2.2. The answer should be bigger than the number we started with.
   10 kg × 2.2
3. Calculate. Use a calculator or work it out carefully.
   10 × 2.2 = 22

Check. Work backwards: 22 ÷ 2.2 ≈ 10. ✓

Watch out. Multiplying and dividing are easy to mix up. Ask yourself: should my answer be a bigger or a smaller number than the one I started with?

Method. Use the given fact to link the two units. To change into the unit with the bigger number multiply; to change back, divide.

1. Write the conversion fact you are given. This tells us how the two units are linked. It is like an exchange rate.
   1 kg ≈ 2.2 pounds
2. Decide: multiply or divide? The fact says 2.2 pounds make 1 kilogram, so the answer is the starting number shared into groups of 2.2: divide by 2.2. The answer should be smaller than the number we started with.
   33 pounds ÷ 2.2
3. Calculate. Use a calculator or work it out carefully.
   33 ÷ 2.2 = 15

Check. Work backwards: 15 × 2.2 ≈ 33. ✓

Watch out. Multiplying and dividing are easy to mix up. Ask yourself: should my answer be a bigger or a smaller number than the one I started with?

Method. Use the given fact to link the two units. To change into the unit with the bigger number multiply; to change back, divide.

1. Write the conversion fact you are given. This tells us how the two units are linked. It is like an exchange rate.
   1 foot = 12 inches
2. Decide: multiply or divide? The fact says 1 foot gives 12 inches, so the answer is 12 times the starting number: multiply by 12. The answer should be bigger than the number we started with.
   4 feet × 12
3. Calculate. Use a calculator or work it out carefully.
   4 × 12 = 48

Check. Work backwards: 48 ÷ 12 = 4. ✓

Watch out. Multiplying and dividing are easy to mix up. Ask yourself: should my answer be a bigger or a smaller number than the one I started with?

Method. Use the given fact to link the two units. To change into the unit with the bigger number multiply; to change back, divide.

1. Write the conversion fact you are given. This tells us how the two units are linked. It is like an exchange rate.
   1 foot = 12 inches
2. Decide: multiply or divide? The fact says 12 inches make 1 foot, so the answer is the starting number shared into groups of 12: divide by 12. The answer should be smaller than the number we started with.
   60 inches ÷ 12
3. Calculate. Use a calculator or work it out carefully.
   60 ÷ 12 = 5

Check. Work backwards: 5 × 12 = 60. ✓

Watch out. Multiplying and dividing are easy to mix up. Ask yourself: should my answer be a bigger or a smaller number than the one I started with?

Method. Use the given fact to link the two units. To change into the unit with the bigger number multiply; to change back, divide.

1. Write the conversion fact you are given. This tells us how the two units are linked. It is like an exchange rate.
   1 yard = 3 feet
2. Decide: multiply or divide? The fact says 1 yard gives 3 feet, so the answer is 3 times the starting number: multiply by 3. The answer should be bigger than the number we started with.
   3 yards × 3
3. Calculate. Use a calculator or work it out carefully.
   3 × 3 = 9

Check. Work backwards: 9 ÷ 3 = 3. ✓

Watch out. Multiplying and dividing are easy to mix up. Ask yourself: should my answer be a bigger or a smaller number than the one I started with?

Method. Use the given fact to link the two units. To change into the unit with the bigger number multiply; to change back, divide.

1. Write the conversion fact you are given. This tells us how the two units are linked. It is like an exchange rate.
   1 stone = 14 pounds
2. Decide: multiply or divide? The fact says 1 stone gives 14 pounds, so the answer is 14 times the starting number: multiply by 14. The answer should be bigger than the number we started with.
   2 stone × 14
3. Calculate. Use a calculator or work it out carefully.
   2 × 14 = 28

Check. Work backwards: 28 ÷ 14 = 2. ✓

Watch out. Multiplying and dividing are easy to mix up. Ask yourself: should my answer be a bigger or a smaller number than the one I started with?

Method. Use the given fact to link the two units. To change into the unit with the bigger number multiply; to change back, divide.

1. Write the conversion fact you are given. This tells us how the two units are linked. It is like an exchange rate.
   1 pound = 16 ounces
2. Decide: multiply or divide? The fact says 16 ounces make 1 pound, so the answer is the starting number shared into groups of 16: divide by 16. The answer should be smaller than the number we started with.
   48 ounces ÷ 16
3. Calculate. Use a calculator or work it out carefully.
   48 ÷ 16 = 3

Check. Work backwards: 3 × 16 = 48. ✓

Watch out. Multiplying and dividing are easy to mix up. Ask yourself: should my answer be a bigger or a smaller number than the one I started with?

Method. Use the given fact to link the two units. To change into the unit with the bigger number multiply; to change back, divide.

1. Write the conversion fact you are given. This tells us how the two units are linked. It is like an exchange rate.
   1 gallon = 8 pints
2. Decide: multiply or divide? The fact says 8 pints make 1 gallon, so the answer is the starting number shared into groups of 8: divide by 8. The answer should be smaller than the number we started with.
   24 pints ÷ 8
3. Calculate. Use a calculator or work it out carefully.
   24 ÷ 8 = 3

Check. Work backwards: 3 × 8 = 24. ✓

Watch out. Multiplying and dividing are easy to mix up. Ask yourself: should my answer be a bigger or a smaller number than the one I started with?

Method. Use the given fact to link the two units. To change into the unit with the bigger number multiply; to change back, divide.

1. Write the conversion fact you are given. This tells us how the two units are linked. It is like an exchange rate.
   £1 = €1.15
2. Decide: multiply or divide? The fact says 1 pound gives 1.15 euros, so the answer is 1.15 times the starting number: multiply by 1.15. The answer should be bigger than the number we started with.
   £40 × 1.15
3. Calculate. Use a calculator or work it out carefully.
   40 × 1.15 = 46

Check. Work backwards: 46 ÷ 1.15 = 40. ✓

Watch out. Multiplying and dividing are easy to mix up. Ask yourself: should my answer be a bigger or a smaller number than the one I started with?

Method. Use the given fact to link the two units. To change into the unit with the bigger number multiply; to change back, divide.

1. Write the conversion fact you are given. This tells us how the two units are linked. It is like an exchange rate.
   £1 = €1.15
2. Decide: multiply or divide? The fact says 1 pound gives 1.15 euros, so the answer is 1.15 times the starting number: multiply by 1.15. The answer should be bigger than the number we started with.
   £225 × 1.15
3. Calculate. Use a calculator or work it out carefully.
   225 × 1.15 = 258.75

Check. Work backwards: 258.75 ÷ 1.15 = 225. ✓

Watch out. Multiplying and dividing are easy to mix up. Ask yourself: should my answer be a bigger or a smaller number than the one I started with?

Method. Use the given fact to link the two units. To change into the unit with the bigger number multiply; to change back, divide.

1. Write the conversion fact you are given. This tells us how the two units are linked. It is like an exchange rate.
   £1 = €1.15
2. Decide: multiply or divide? The fact says 1.15 euros make 1 pound, so the answer is the starting number shared into groups of 1.15: divide by 1.15. The answer should be smaller than the number we started with.
   €92 ÷ 1.15
3. Calculate. Use a calculator or work it out carefully.
   92 ÷ 1.15 = 80

Check. Work backwards: 80 × 1.15 = 92. ✓

Watch out. Multiplying and dividing are easy to mix up. Ask yourself: should my answer be a bigger or a smaller number than the one I started with?

Method. Use the given fact to link the two units. To change into the unit with the bigger number multiply; to change back, divide.

1. Write the conversion fact you are given. This tells us how the two units are linked. It is like an exchange rate.
   £1 = €1.15
2. Decide: multiply or divide? The fact says 1.15 euros make 1 pound, so the answer is the starting number shared into groups of 1.15: divide by 1.15. The answer should be smaller than the number we started with.
   €172.50 ÷ 1.15
3. Calculate. Use a calculator or work it out carefully.
   172.5 ÷ 1.15 = 150

Check. Work backwards: 150 × 1.15 = 172.5. ✓

Watch out. Multiplying and dividing are easy to mix up. Ask yourself: should my answer be a bigger or a smaller number than the one I started with?

Method. Use the given fact to link the two units. To change into the unit with the bigger number multiply; to change back, divide.

1. Write the conversion fact you are given. This tells us how the two units are linked. It is like an exchange rate.
   £1 = $1.25
2. Decide: multiply or divide? The fact says 1 pound gives 1.25 dollars, so the answer is 1.25 times the starting number: multiply by 1.25. The answer should be bigger than the number we started with.
   £64 × 1.25
3. Calculate. Use a calculator or work it out carefully.
   64 × 1.25 = 80

Check. Work backwards: 80 ÷ 1.25 = 64. ✓

Watch out. Multiplying and dividing are easy to mix up. Ask yourself: should my answer be a bigger or a smaller number than the one I started with?

Method. Use the given fact to link the two units. To change into the unit with the bigger number multiply; to change back, divide.

1. Write the conversion fact you are given. This tells us how the two units are linked. It is like an exchange rate.
   £1 = $1.25
2. Decide: multiply or divide? The fact says 1.25 dollars make 1 pound, so the answer is the starting number shared into groups of 1.25: divide by 1.25. The answer should be smaller than the number we started with.
   $135 ÷ 1.25
3. Calculate. Use a calculator or work it out carefully.
   135 ÷ 1.25 = 108

Check. Work backwards: 108 × 1.25 = 135. ✓

Watch out. Multiplying and dividing are easy to mix up. Ask yourself: should my answer be a bigger or a smaller number than the one I started with?

Method. Use the given fact to link the two units. To change into the unit with the bigger number multiply; to change back, divide.

1. Write the conversion fact you are given. This tells us how the two units are linked. It is like an exchange rate.
   £1 = $1.25
2. Decide: multiply or divide? The fact says 1 pound gives 1.25 dollars, so the answer is 1.25 times the starting number: multiply by 1.25. The answer should be bigger than the number we started with.
   £18.40 × 1.25
3. Calculate. Use a calculator or work it out carefully.
   18.4 × 1.25 = 23

Check. Work backwards: 23 ÷ 1.25 = 18.4. ✓

Watch out. Multiplying and dividing are easy to mix up. Ask yourself: should my answer be a bigger or a smaller number than the one I started with?

Method. Change stones to pounds and add the extra.

1. Stones to pounds. 1 stone = 14 pounds, so multiply by 14.
   12 × 14 = 168 pounds
2. Add the 6 pounds. Do not forget the extra pounds.
   168 + 6 = 174 pounds

Check. 174 ÷ 14 = 12 remainder 6. ✓

Method. Pounds to kilograms: divide by 2.2.

1. Write the fact. This links kilograms and pounds.
   1 kg ≈ 2.2 pounds
2. Divide. There are fewer kilograms than pounds.
   174 ÷ 2.2 = 79.0909
3. Round to 1 d.p. The question asks for 1 decimal place.
   79.1 kg

Check. 79.1 × 2.2 ≈ 174. ✓

Key words. Speed tells you how far something travels in one unit of time. Average speed is the total distance divided by the total time.

Method. Use the formula triangle for distance, speed and time: distance = speed × time. Cover what you want to find to see the calculation.

1. Write down what you know and what you want. Always list the quantities with their units before you start.
   We know the distance (120 km) and the time (2 hours).
   We want the speed.
2. Choose the formula. Cover the quantity you want in the formula triangle. What is left tells you whether to multiply or divide.
   speed = distance ÷ time
3. Put the numbers in and calculate. Use the values with matching units.
   speed = 120 ÷ 2 = 60
4. Write the answer with its unit. The unit is km/h.
   speed = 60 km/h

Check. Work backwards: 60 × 2 = 120 (the distance). ✓

Watch out. Check the units match before you calculate (for example, minutes must be changed to hours if the speed is per hour).

Key words. Speed tells you how far something travels in one unit of time. Average speed is the total distance divided by the total time.

Method. Use the formula triangle for distance, speed and time: distance = speed × time. Cover what you want to find to see the calculation.

1. Write down what you know and what you want. Always list the quantities with their units before you start.
   We know the distance (90 miles) and the time (1.5 hours).
   We want the speed.
2. Choose the formula. Cover the quantity you want in the formula triangle. What is left tells you whether to multiply or divide.
   speed = distance ÷ time
3. Put the numbers in and calculate. Use the values with matching units.
   speed = 90 ÷ 1.5 = 60
4. Write the answer with its unit. The unit is mph.
   speed = 60 mph

Check. Work backwards: 60 × 1.5 = 90 (the distance). ✓

Watch out. Check the units match before you calculate (for example, minutes must be changed to hours if the speed is per hour).

Key words. Speed tells you how far something travels in one unit of time. Average speed is the total distance divided by the total time.

Method. Use the formula triangle for distance, speed and time: distance = speed × time. Cover what you want to find to see the calculation.

1. Write down what you know and what you want. Always list the quantities with their units before you start.
   We know the distance (200 m) and the time (25 seconds).
   We want the speed.
2. Choose the formula. Cover the quantity you want in the formula triangle. What is left tells you whether to multiply or divide.
   speed = distance ÷ time
3. Put the numbers in and calculate. Use the values with matching units.
   speed = 200 ÷ 25 = 8
4. Write the answer with its unit. The unit is m/s.
   speed = 8 m/s

Check. Work backwards: 8 × 25 = 200 (the distance). ✓

Watch out. Check the units match before you calculate (for example, minutes must be changed to hours if the speed is per hour).

Key words. Speed tells you how far something travels in one unit of time. Average speed is the total distance divided by the total time.

Method. Use the formula triangle for distance, speed and time: distance = speed × time. Cover what you want to find to see the calculation.

1. Change the time to hours. The speed is in km per hour, so the time must be in hours. There are 60 minutes in 1 hour, so divide by 60.
   30 minutes = 30 ÷ 60 = 0.5 hours
2. Write down what you know and what you want. Always list the quantities with their units before you start.
   We know the distance (15 km) and the time (0.5 hours).
   We want the speed.
3. Choose the formula. Cover the quantity you want in the formula triangle. What is left tells you whether to multiply or divide.
   speed = distance ÷ time
4. Put the numbers in and calculate. Use the values with matching units.
   speed = 15 ÷ 0.5 = 30
5. Write the answer with its unit. The unit is km/h.
   speed = 30 km/h

Check. Work backwards: 30 × 0.5 = 15 (the distance). ✓

Watch out. Check the units match before you calculate (for example, minutes must be changed to hours if the speed is per hour).

Key words. Speed tells you how far something travels in one unit of time. Average speed is the total distance divided by the total time.

Method. Use the formula triangle for distance, speed and time: distance = speed × time. Cover what you want to find to see the calculation.

1. Write down what you know and what you want. Always list the quantities with their units before you start.
   We know the distance (450 km) and the time (5 hours).
   We want the speed.
2. Choose the formula. Cover the quantity you want in the formula triangle. What is left tells you whether to multiply or divide.
   speed = distance ÷ time
3. Put the numbers in and calculate. Use the values with matching units.
   speed = 450 ÷ 5 = 90
4. Write the answer with its unit. The unit is km/h.
   speed = 90 km/h

Check. Work backwards: 90 × 5 = 450 (the distance). ✓

Watch out. Check the units match before you calculate (for example, minutes must be changed to hours if the speed is per hour).

Key words. Speed tells you how far something travels in one unit of time. Average speed is the total distance divided by the total time.

Method. Use the formula triangle for distance, speed and time: distance = speed × time. Cover what you want to find to see the calculation.

1. Change the time to hours. The speed is in miles per hour, so the time must be in hours. There are 60 minutes in 1 hour, so divide by 60.
   45 minutes = 45 ÷ 60 = 0.75 hours
2. Write down what you know and what you want. Always list the quantities with their units before you start.
   We know the distance (18 miles) and the time (0.75 hours).
   We want the speed.
3. Choose the formula. Cover the quantity you want in the formula triangle. What is left tells you whether to multiply or divide.
   speed = distance ÷ time
4. Put the numbers in and calculate. Use the values with matching units.
   speed = 18 ÷ 0.75 = 24
5. Write the answer with its unit. The unit is mph.
   speed = 24 mph

Check. Work backwards: 24 × 0.75 = 18 (the distance). ✓

Watch out. Check the units match before you calculate (for example, minutes must be changed to hours if the speed is per hour).

Key words. Speed tells you how far something travels in one unit of time. Average speed is the total distance divided by the total time.

Method. Use the formula triangle for distance, speed and time: distance = speed × time. Cover what you want to find to see the calculation.

1. Write down what you know and what you want. Always list the quantities with their units before you start.
   We know the speed (60 km/h) and the time (3 hours).
   We want the distance.
2. Choose the formula. Cover the quantity you want in the formula triangle. What is left tells you whether to multiply or divide.
   distance = speed × time
3. Put the numbers in and calculate. Use the values with matching units.
   distance = 60 × 3 = 180
4. Write the answer with its unit. The unit is km.
   distance = 180 km

Check. Work backwards: 180 ÷ 3 = 60 (the speed). ✓

Watch out. Check the units match before you calculate (for example, minutes must be changed to hours if the speed is per hour).

Key words. Speed tells you how far something travels in one unit of time. Average speed is the total distance divided by the total time.

Method. Use the formula triangle for distance, speed and time: distance = speed × time. Cover what you want to find to see the calculation.

1. Write down what you know and what you want. Always list the quantities with their units before you start.
   We know the speed (40 mph) and the time (2.5 hours).
   We want the distance.
2. Choose the formula. Cover the quantity you want in the formula triangle. What is left tells you whether to multiply or divide.
   distance = speed × time
3. Put the numbers in and calculate. Use the values with matching units.
   distance = 40 × 2.5 = 100
4. Write the answer with its unit. The unit is miles.
   distance = 100 miles

Check. Work backwards: 100 ÷ 2.5 = 40 (the speed). ✓

Watch out. Check the units match before you calculate (for example, minutes must be changed to hours if the speed is per hour).

Key words. Speed tells you how far something travels in one unit of time. Average speed is the total distance divided by the total time.

Method. Use the formula triangle for distance, speed and time: distance = speed × time. Cover what you want to find to see the calculation.

1. Write down what you know and what you want. Always list the quantities with their units before you start.
   We know the speed (8 m/s) and the time (15 seconds).
   We want the distance.
2. Choose the formula. Cover the quantity you want in the formula triangle. What is left tells you whether to multiply or divide.
   distance = speed × time
3. Put the numbers in and calculate. Use the values with matching units.
   distance = 8 × 15 = 120
4. Write the answer with its unit. The unit is m.
   distance = 120 m

Check. Work backwards: 120 ÷ 15 = 8 (the speed). ✓

Watch out. Check the units match before you calculate (for example, minutes must be changed to hours if the speed is per hour).

Key words. Speed tells you how far something travels in one unit of time. Average speed is the total distance divided by the total time.

Method. Use the formula triangle for distance, speed and time: distance = speed × time. Cover what you want to find to see the calculation.

1. Change the time to hours. The speed is in km per hour, so the time must be in hours. There are 60 minutes in 1 hour, so divide by 60.
   12 minutes = 12 ÷ 60 = 0.2 hours
2. Write down what you know and what you want. Always list the quantities with their units before you start.
   We know the speed (80 km/h) and the time (0.2 hours).
   We want the distance.
3. Choose the formula. Cover the quantity you want in the formula triangle. What is left tells you whether to multiply or divide.
   distance = speed × time
4. Put the numbers in and calculate. Use the values with matching units.
   distance = 80 × 0.2 = 16
5. Write the answer with its unit. The unit is km.
   distance = 16 km

Check. Work backwards: 16 ÷ 0.2 = 80 (the speed). ✓

Watch out. Check the units match before you calculate (for example, minutes must be changed to hours if the speed is per hour).

Key words. Speed tells you how far something travels in one unit of time. Average speed is the total distance divided by the total time.

Method. Use the formula triangle for distance, speed and time: distance = speed × time. Cover what you want to find to see the calculation.

1. Change the time to hours. The speed is in km per hour, so the time must be in hours. There are 60 minutes in 1 hour, so divide by 60.
   45 minutes = 45 ÷ 60 = 0.75 hours
2. Write down what you know and what you want. Always list the quantities with their units before you start.
   We know the speed (36 km/h) and the time (0.75 hours).
   We want the distance.
3. Choose the formula. Cover the quantity you want in the formula triangle. What is left tells you whether to multiply or divide.
   distance = speed × time
4. Put the numbers in and calculate. Use the values with matching units.
   distance = 36 × 0.75 = 27
5. Write the answer with its unit. The unit is km.
   distance = 27 km

Check. Work backwards: 27 ÷ 0.75 = 36 (the speed). ✓

Watch out. Check the units match before you calculate (for example, minutes must be changed to hours if the speed is per hour).

Key words. Speed tells you how far something travels in one unit of time. Average speed is the total distance divided by the total time.

Method. Use the formula triangle for distance, speed and time: distance = speed × time. Cover what you want to find to see the calculation.

1. Change the time to hours. The speed is in km per hour, so the time must be in hours. There are 60 minutes in 1 hour, so divide by 60.
   15 minutes = 15 ÷ 60 = 0.25 hours
2. Write down what you know and what you want. Always list the quantities with their units before you start.
   We know the speed (72 km/h) and the time (0.25 hours).
   We want the distance.
3. Choose the formula. Cover the quantity you want in the formula triangle. What is left tells you whether to multiply or divide.
   distance = speed × time
4. Put the numbers in and calculate. Use the values with matching units.
   distance = 72 × 0.25 = 18
5. Write the answer with its unit. The unit is km.
   distance = 18 km

Check. Work backwards: 18 ÷ 0.25 = 72 (the speed). ✓

Watch out. Check the units match before you calculate (for example, minutes must be changed to hours if the speed is per hour).

Key words. Speed tells you how far something travels in one unit of time. Average speed is the total distance divided by the total time.

Method. Use the formula triangle for distance, speed and time: distance = speed × time. Cover what you want to find to see the calculation.

1. Write down what you know and what you want. Always list the quantities with their units before you start.
   We know the distance (180 km) and the speed (60 km/h).
   We want the time.
2. Choose the formula. Cover the quantity you want in the formula triangle. What is left tells you whether to multiply or divide.
   time = distance ÷ speed
3. Put the numbers in and calculate. Use the values with matching units.
   time = 180 ÷ 60 = 3
4. Write the answer with its unit. The unit is hours.
   time = 3 hours

Check. Work backwards: 60 × 3 = 180 (the distance). ✓

Watch out. Check the units match before you calculate (for example, minutes must be changed to hours if the speed is per hour).

Key words. Speed tells you how far something travels in one unit of time. Average speed is the total distance divided by the total time.

Method. Use the formula triangle for distance, speed and time: distance = speed × time. Cover what you want to find to see the calculation.

1. Write down what you know and what you want. Always list the quantities with their units before you start.
   We know the distance (150 miles) and the speed (40 mph).
   We want the time.
2. Choose the formula. Cover the quantity you want in the formula triangle. What is left tells you whether to multiply or divide.
   time = distance ÷ speed
3. Put the numbers in and calculate. Use the values with matching units.
   time = 150 ÷ 40 = 3.75
4. Change the decimal hours to hours and minutes. The decimal part of an hour is multiplied by 60 to get minutes.
   0.75 × 60 = 45 minutes
   3.75 hours = 3 hours 45 minutes
5. Write the answer with its unit. The unit is hours.
   time = 3.75 hours

Check. Work backwards: 40 × 3.75 = 150 (the distance). ✓

Watch out. Check the units match before you calculate (for example, minutes must be changed to hours if the speed is per hour).

Key words. Speed tells you how far something travels in one unit of time. Average speed is the total distance divided by the total time.

Method. Use the formula triangle for distance, speed and time: distance = speed × time. Cover what you want to find to see the calculation.

1. Write down what you know and what you want. Always list the quantities with their units before you start.
   We know the distance (100 m) and the speed (8 m/s).
   We want the time.
2. Choose the formula. Cover the quantity you want in the formula triangle. What is left tells you whether to multiply or divide.
   time = distance ÷ speed
3. Put the numbers in and calculate. Use the values with matching units.
   time = 100 ÷ 8 = 12.5
4. Write the answer with its unit. The unit is seconds.
   time = 12.5 seconds

Check. Work backwards: 8 × 12.5 = 100 (the distance). ✓

Watch out. Check the units match before you calculate (for example, minutes must be changed to hours if the speed is per hour).

Key words. Speed tells you how far something travels in one unit of time. Average speed is the total distance divided by the total time.

Method. Use the formula triangle for distance, speed and time: distance = speed × time. Cover what you want to find to see the calculation.

1. Write down what you know and what you want. Always list the quantities with their units before you start.
   We know the distance (90 km) and the speed (36 km/h).
   We want the time.
2. Choose the formula. Cover the quantity you want in the formula triangle. What is left tells you whether to multiply or divide.
   time = distance ÷ speed
3. Put the numbers in and calculate. Use the values with matching units.
   time = 90 ÷ 36 = 2.5
4. Change the decimal hours to hours and minutes. The decimal part of an hour is multiplied by 60 to get minutes.
   0.5 × 60 = 30 minutes
   2.5 hours = 2 hours 30 minutes
5. Write the answer with its unit. The unit is hours.
   time = 2.5 hours

Check. Work backwards: 36 × 2.5 = 90 (the distance). ✓

Watch out. Check the units match before you calculate (for example, minutes must be changed to hours if the speed is per hour).

Key words. Speed tells you how far something travels in one unit of time. Average speed is the total distance divided by the total time.

Method. Use the formula triangle for distance, speed and time: distance = speed × time. Cover what you want to find to see the calculation.

1. Write down what you know and what you want. Always list the quantities with their units before you start.
   We know the distance (45 km) and the speed (30 km/h).
   We want the time.
2. Choose the formula. Cover the quantity you want in the formula triangle. What is left tells you whether to multiply or divide.
   time = distance ÷ speed
3. Put the numbers in and calculate. Use the values with matching units.
   time = 45 ÷ 30 = 1.5
4. Change the decimal hours to hours and minutes. The decimal part of an hour is multiplied by 60 to get minutes.
   0.5 × 60 = 30 minutes
   1.5 hours = 1 hours 30 minutes
5. Write the answer with its unit. The unit is hours.
   time = 1.5 hours

Check. Work backwards: 30 × 1.5 = 45 (the distance). ✓

Watch out. Check the units match before you calculate (for example, minutes must be changed to hours if the speed is per hour).

Key words. Speed tells you how far something travels in one unit of time. Average speed is the total distance divided by the total time.

Method. Use the formula triangle for distance, speed and time: distance = speed × time. Cover what you want to find to see the calculation.

1. Write down what you know and what you want. Always list the quantities with their units before you start.
   We know the distance (270 km) and the speed (72 km/h).
   We want the time.
2. Choose the formula. Cover the quantity you want in the formula triangle. What is left tells you whether to multiply or divide.
   time = distance ÷ speed
3. Put the numbers in and calculate. Use the values with matching units.
   time = 270 ÷ 72 = 3.75
4. Change the decimal hours to hours and minutes. The decimal part of an hour is multiplied by 60 to get minutes.
   0.75 × 60 = 45 minutes
   3.75 hours = 3 hours 45 minutes
5. Write the answer with its unit. The unit is hours.
   time = 3.75 hours

Check. Work backwards: 72 × 3.75 = 270 (the distance). ✓

Watch out. Check the units match before you calculate (for example, minutes must be changed to hours if the speed is per hour).

Method. Together they close the gap at a combined speed, so add the speeds.

1. Add the speeds. Each hour the gap shrinks by 18 km (Amy) plus 12 km (Ben).
   18 + 12 = 30 km/h
2. Divide the gap by the closing speed. Time = distance ÷ speed.
   90 ÷ 30 = 3 hours

Check. In 3 hours Amy rides 54 km and Ben rides 36 km: 54 + 36 = 90. ✓

Method. Use distance = speed × time with the time you found.

1. Write the formula. Distance = speed × time.
   D = 18 × 3
2. Calculate.
   18 × 3 = 54 km

Check. 90 − 54 = 36 km, which is how far Ben rode (12 × 3). ✓

Method. Change kilometres to metres and hours to seconds. 1 km = 1000 m and 1 hour = 3600 seconds.

1. Change the kilometres to metres. Metres are smaller than km, so multiply by 1000.
   36 km = 36 × 1000 = 36,000 m
   so 36 km/h = 36,000 metres per hour
2. Change the hour to seconds. 1 hour = 60 × 60 = 3600 seconds. In one second the car goes 3600 times less far, so divide by 3600.
   36,000 ÷ 3600 = 10 metres per second
3. Write the answer.
   36 km/h = 10 m/s

Check. Shortcut: km/h ÷ 3.6 gives m/s: 36 ÷ 3.6 = 10. ✓

Watch out. You are dividing by 3600 for the time but multiplying by 1000 for the distance. Both parts are needed.

Method. Change kilometres to metres and hours to seconds. 1 km = 1000 m and 1 hour = 3600 seconds.

1. Change the kilometres to metres. Metres are smaller than km, so multiply by 1000.
   54 km = 54 × 1000 = 54,000 m
   so 54 km/h = 54,000 metres per hour
2. Change the hour to seconds. 1 hour = 60 × 60 = 3600 seconds. In one second the car goes 3600 times less far, so divide by 3600.
   54,000 ÷ 3600 = 15 metres per second
3. Write the answer.
   54 km/h = 15 m/s

Check. Shortcut: km/h ÷ 3.6 gives m/s: 54 ÷ 3.6 = 15. ✓

Watch out. You are dividing by 3600 for the time but multiplying by 1000 for the distance. Both parts are needed.

Method. Change kilometres to metres and hours to seconds. 1 km = 1000 m and 1 hour = 3600 seconds.

1. Change the kilometres to metres. Metres are smaller than km, so multiply by 1000.
   90 km = 90 × 1000 = 90,000 m
   so 90 km/h = 90,000 metres per hour
2. Change the hour to seconds. 1 hour = 60 × 60 = 3600 seconds. In one second the car goes 3600 times less far, so divide by 3600.
   90,000 ÷ 3600 = 25 metres per second
3. Write the answer.
   90 km/h = 25 m/s

Check. Shortcut: km/h ÷ 3.6 gives m/s: 90 ÷ 3.6 = 25. ✓

Watch out. You are dividing by 3600 for the time but multiplying by 1000 for the distance. Both parts are needed.

Method. Change kilometres to metres and hours to seconds. 1 km = 1000 m and 1 hour = 3600 seconds.

1. Change the kilometres to metres. Metres are smaller than km, so multiply by 1000.
   144 km = 144 × 1000 = 144,000 m
   so 144 km/h = 144,000 metres per hour
2. Change the hour to seconds. 1 hour = 60 × 60 = 3600 seconds. In one second the car goes 3600 times less far, so divide by 3600.
   144,000 ÷ 3600 = 40 metres per second
3. Write the answer.
   144 km/h = 40 m/s

Check. Shortcut: km/h ÷ 3.6 gives m/s: 144 ÷ 3.6 = 40. ✓

Watch out. You are dividing by 3600 for the time but multiplying by 1000 for the distance. Both parts are needed.

Method. Change metres to kilometres and seconds to hours. In one hour there are 3600 seconds, so the object travels 3600 times as far.

1. Find the distance in one hour in metres. There are 3600 seconds in 1 hour, so multiply by 3600.
   5 m/s = 5 × 3600 = 18,000 metres per hour
2. Change metres to kilometres. 1000 m = 1 km, so divide by 1000.
   18,000 ÷ 1000 = 18 km per hour
3. Write the answer.
   5 m/s = 18 km/h

Check. Shortcut: m/s × 3.6 gives km/h: 5 × 3.6 = 18. ✓

Watch out. m/s to km/h makes the number bigger. A km/h number is always bigger than the m/s number for the same speed.

Method. Change metres to kilometres and seconds to hours. In one hour there are 3600 seconds, so the object travels 3600 times as far.

1. Find the distance in one hour in metres. There are 3600 seconds in 1 hour, so multiply by 3600.
   12 m/s = 12 × 3600 = 43,200 metres per hour
2. Change metres to kilometres. 1000 m = 1 km, so divide by 1000.
   43,200 ÷ 1000 = 43.2 km per hour
3. Write the answer.
   12 m/s = 43.2 km/h

Check. Shortcut: m/s × 3.6 gives km/h: 12 × 3.6 = 43.2. ✓

Watch out. m/s to km/h makes the number bigger. A km/h number is always bigger than the m/s number for the same speed.

Method. Change metres to kilometres and seconds to hours. In one hour there are 3600 seconds, so the object travels 3600 times as far.

1. Find the distance in one hour in metres. There are 3600 seconds in 1 hour, so multiply by 3600.
   25 m/s = 25 × 3600 = 90,000 metres per hour
2. Change metres to kilometres. 1000 m = 1 km, so divide by 1000.
   90,000 ÷ 1000 = 90 km per hour
3. Write the answer.
   25 m/s = 90 km/h

Check. Shortcut: m/s × 3.6 gives km/h: 25 × 3.6 = 90. ✓

Watch out. m/s to km/h makes the number bigger. A km/h number is always bigger than the m/s number for the same speed.

Method. Change metres to kilometres and seconds to hours. In one hour there are 3600 seconds, so the object travels 3600 times as far.

1. Find the distance in one hour in metres. There are 3600 seconds in 1 hour, so multiply by 3600.
   40 m/s = 40 × 3600 = 144,000 metres per hour
2. Change metres to kilometres. 1000 m = 1 km, so divide by 1000.
   144,000 ÷ 1000 = 144 km per hour
3. Write the answer.
   40 m/s = 144 km/h

Check. Shortcut: m/s × 3.6 gives km/h: 40 × 3.6 = 144. ✓

Watch out. m/s to km/h makes the number bigger. A km/h number is always bigger than the m/s number for the same speed.

Method. Average speed = total distance ÷ total time. Do not average the speeds themselves.

1. Add the distances. Average speed uses the total distance.
   24 + 36 = 60 km
2. Add the times. It also uses the total time, including any stops that are part of the journey.
   30 + 30 = 60 minutes
3. Change the total time to hours. We want a speed in per hour, so the time must be in hours: divide minutes by 60.
   60 ÷ 60 = 1 hour
4. Divide total distance by total time. speed = distance ÷ time.
   60 ÷ 1 = 60
5. Write the answer with its unit.
   average speed = 60 km/h

Check. Work backwards: 60 × 1 = 60 km, which is the total distance. ✓

Watch out. Do not add the speeds and halve them. A slow part that lasts a long time counts for more.

Method. Average speed = total distance ÷ total time. Do not average the speeds themselves.

1. Add the distances. Average speed uses the total distance.
   20 + 30 = 50 km
2. Add the times. It also uses the total time, including any stops that are part of the journey.
   24 + 36 = 60 minutes
3. Change the total time to hours. We want a speed in per hour, so the time must be in hours: divide minutes by 60.
   60 ÷ 60 = 1 hour
4. Divide total distance by total time. speed = distance ÷ time.
   50 ÷ 1 = 50
5. Write the answer with its unit.
   average speed = 50 km/h

Check. Work backwards: 50 × 1 = 50 km, which is the total distance. ✓

Watch out. Do not add the speeds and halve them. A slow part that lasts a long time counts for more.

Method. Average speed = total distance ÷ total time. Do not average the speeds themselves.

1. Add the distances. Average speed uses the total distance.
   30 + 10 = 40 km
2. Add the times. It also uses the total time, including any stops that are part of the journey.
   45 + 15 = 60 minutes
3. Change the total time to hours. We want a speed in per hour, so the time must be in hours: divide minutes by 60.
   60 ÷ 60 = 1 hour
4. Divide total distance by total time. speed = distance ÷ time.
   40 ÷ 1 = 40
5. Write the answer with its unit.
   average speed = 40 km/h

Check. Work backwards: 40 × 1 = 40 km, which is the total distance. ✓

Watch out. Do not add the speeds and halve them. A slow part that lasts a long time counts for more.

Method. Average speed = total distance ÷ total time. Do not average the speeds themselves.

1. Add the distances. Average speed uses the total distance.
   45 + 25 = 70 km
2. Add the times. It also uses the total time, including any stops that are part of the journey.
   30 + 30 = 60 minutes
3. Change the total time to hours. We want a speed in per hour, so the time must be in hours: divide minutes by 60.
   60 ÷ 60 = 1 hour
4. Divide total distance by total time. speed = distance ÷ time.
   70 ÷ 1 = 70
5. Write the answer with its unit.
   average speed = 70 km/h

Check. Work backwards: 70 × 1 = 70 km, which is the total distance. ✓

Watch out. Do not add the speeds and halve them. A slow part that lasts a long time counts for more.

Method. Use the whole time (including the stop): 09:00 to 11:30 is 2.5 hours.

1. Find the total time. 09:00 to 11:30 is 2 hours 30 minutes.
   2 hours 30 minutes = 2.5 hours
2. Divide. Speed = distance ÷ time.
   135 ÷ 2.5 = 54 mph

Check. 54 × 2.5 = 135. ✓

Method. Take the 30 minute stop away from the time first.

1. Find the moving time. The coach is stopped for 0.5 hours.
   2.5 − 0.5 = 2 hours
2. Divide. Speed = distance ÷ time.
   135 ÷ 2 = 67.5 mph

Check. 67.5 × 2 = 135. ✓

Watch out. Average speed for the whole journey includes stops; the speed while moving does not.