GCSE Maths: Units of measure, time and money (Foundation)

Key words. A unit says what we measure in. Metric units are based on 10, 100 and 1000, so converting means multiplying or dividing by powers of 10.

Method. To change units, use the conversion fact. Change to a smaller unit: multiply. Change to a bigger unit: divide.

1. Write down the conversion fact. We need to know how many of the smaller unit make one of the bigger unit.
   1 m = 100 cm
2. Decide: m to cm means changing to a smaller unit, so multiply. A smaller unit means you need more of them. For example 2 m is 200 cm. So we multiply by 100.
   3.5 m × 100
3. Calculate.
   3.5 × 100 = 350
4. Write the answer with its unit. Always put the new unit in the answer.
   3.5 m = 350 cm

Check. Convert back: 350 ÷ 100 = 3.5. ✓

Watch out. Check the direction: there are always more of the smaller unit. If your answer for centimetres is smaller than the number of metres, you divided when you should have multiplied.

Key words. A unit says what we measure in. Metric units are based on 10, 100 and 1000, so converting means multiplying or dividing by powers of 10.

Method. To change units, use the conversion fact. Change to a smaller unit: multiply. Change to a bigger unit: divide.

1. Write down the conversion fact. We need to know how many of the smaller unit make one of the bigger unit.
   1 m = 100 cm
2. Decide: cm to m means changing to a bigger unit, so divide. A bigger unit means you need fewer of them. For example 200 cm is only 2 m. So we divide by 100.
   450 cm ÷ 100
3. Calculate. Dividing by 10, 100 or 1000 moves each digit to the right.
   450 ÷ 100 = 4.5
4. Write the answer with its unit. Always put the new unit in the answer.
   450 cm = 4.5 m

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

Watch out. Check the direction: there are always more of the smaller unit. If your answer for centimetres is smaller than the number of metres, you divided when you should have multiplied.

Key words. A unit says what we measure in. Metric units are based on 10, 100 and 1000, so converting means multiplying or dividing by powers of 10.

Method. To change units, use the conversion fact. Change to a smaller unit: multiply. Change to a bigger unit: divide.

1. Write down the conversion fact. We need to know how many of the smaller unit make one of the bigger unit.
   1 km = 1000 m
2. Decide: km to m means changing to a smaller unit, so multiply. A smaller unit means you need more of them. For example 2 km is 2000 m. So we multiply by 1000.
   2.4 km × 1000
3. Calculate.
   2.4 × 1000 = 2400
4. Write the answer with its unit. Always put the new unit in the answer.
   2.4 km = 2400 m

Check. Convert back: 2400 ÷ 1000 = 2.4. ✓

Watch out. Check the direction: there are always more of the smaller unit. If your answer for centimetres is smaller than the number of metres, you divided when you should have multiplied.

Key words. A unit says what we measure in. Metric units are based on 10, 100 and 1000, so converting means multiplying or dividing by powers of 10.

Method. To change units, use the conversion fact. Change to a smaller unit: multiply. Change to a bigger unit: divide.

1. Write down the conversion fact. We need to know how many of the smaller unit make one of the bigger unit.
   1 km = 1000 m
2. Decide: m to km means changing to a bigger unit, so divide. A bigger unit means you need fewer of them. For example 2000 m is only 2 km. So we divide by 1000.
   7500 m ÷ 1000
3. Calculate. Dividing by 10, 100 or 1000 moves each digit to the right.
   7500 ÷ 1000 = 7.5
4. Write the answer with its unit. Always put the new unit in the answer.
   7500 m = 7.5 km

Check. Convert back: 7.5 × 1000 = 7500. ✓

Watch out. Check the direction: there are always more of the smaller unit. If your answer for centimetres is smaller than the number of metres, you divided when you should have multiplied.

Key words. A unit says what we measure in. Metric units are based on 10, 100 and 1000, so converting means multiplying or dividing by powers of 10.

Method. To change units, use the conversion fact. Change to a smaller unit: multiply. Change to a bigger unit: divide.

1. Write down the conversion fact. We need to know how many of the smaller unit make one of the bigger unit.
   1 cm = 10 mm
2. Decide: mm to cm means changing to a bigger unit, so divide. A bigger unit means you need fewer of them. For example 20 mm is only 2 cm. So we divide by 10.
   85 mm ÷ 10
3. Calculate. Dividing by 10, 100 or 1000 moves each digit to the right.
   85 ÷ 10 = 8.5
4. Write the answer with its unit. Always put the new unit in the answer.
   85 mm = 8.5 cm

Check. Convert back: 8.5 × 10 = 85. ✓

Watch out. Check the direction: there are always more of the smaller unit. If your answer for centimetres is smaller than the number of metres, you divided when you should have multiplied.

Key words. A unit says what we measure in. Metric units are based on 10, 100 and 1000, so converting means multiplying or dividing by powers of 10.

Method. To change units, use the conversion fact. Change to a smaller unit: multiply. Change to a bigger unit: divide.

1. Write down the conversion fact. We need to know how many of the smaller unit make one of the bigger unit.
   1 m = 1000 mm
2. Decide: m to mm means changing to a smaller unit, so multiply. A smaller unit means you need more of them. For example 2 m is 2000 mm. So we multiply by 1000.
   0.6 m × 1000
3. Calculate.
   0.6 × 1000 = 600
4. Write the answer with its unit. Always put the new unit in the answer.
   0.6 m = 600 mm

Check. Convert back: 600 ÷ 1000 = 0.6. ✓

Watch out. Check the direction: there are always more of the smaller unit. If your answer for centimetres is smaller than the number of metres, you divided when you should have multiplied.

Key words. A unit says what we measure in. Metric units are based on 10, 100 and 1000, so converting means multiplying or dividing by powers of 10.

Method. To change units, use the conversion fact. Change to a smaller unit: multiply. Change to a bigger unit: divide.

1. Write down the conversion fact. We need to know how many of the smaller unit make one of the bigger unit.
   1 kg = 1000 g
2. Decide: kg to g means changing to a smaller unit, so multiply. A smaller unit means you need more of them. For example 2 kg is 2000 g. So we multiply by 1000.
   2.5 kg × 1000
3. Calculate.
   2.5 × 1000 = 2500
4. Write the answer with its unit. Always put the new unit in the answer.
   2.5 kg = 2500 g

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

Watch out. Check the direction: there are always more of the smaller unit. If your answer for centimetres is smaller than the number of metres, you divided when you should have multiplied.

Key words. A unit says what we measure in. Metric units are based on 10, 100 and 1000, so converting means multiplying or dividing by powers of 10.

Method. To change units, use the conversion fact. Change to a smaller unit: multiply. Change to a bigger unit: divide.

1. Write down the conversion fact. We need to know how many of the smaller unit make one of the bigger unit.
   1 kg = 1000 g
2. Decide: g to kg means changing to a bigger unit, so divide. A bigger unit means you need fewer of them. For example 2000 g is only 2 kg. So we divide by 1000.
   3400 g ÷ 1000
3. Calculate. Dividing by 10, 100 or 1000 moves each digit to the right.
   3400 ÷ 1000 = 3.4
4. Write the answer with its unit. Always put the new unit in the answer.
   3400 g = 3.4 kg

Check. Convert back: 3.4 × 1000 = 3400. ✓

Watch out. Check the direction: there are always more of the smaller unit. If your answer for centimetres is smaller than the number of metres, you divided when you should have multiplied.

Key words. A unit says what we measure in. Metric units are based on 10, 100 and 1000, so converting means multiplying or dividing by powers of 10.

Method. To change units, use the conversion fact. Change to a smaller unit: multiply. Change to a bigger unit: divide.

1. Write down the conversion fact. We need to know how many of the smaller unit make one of the bigger unit.
   1 litre = 1000 ml
2. Decide: litre to ml means changing to a smaller unit, so multiply. A smaller unit means you need more of them. For example 2 litres is 2000 ml. So we multiply by 1000.
   0.75 litres × 1000
3. Calculate.
   0.75 × 1000 = 750
4. Write the answer with its unit. Always put the new unit in the answer.
   0.75 litres = 750 ml

Check. Convert back: 750 ÷ 1000 = 0.75. ✓

Watch out. Check the direction: there are always more of the smaller unit. If your answer for centimetres is smaller than the number of metres, you divided when you should have multiplied.

Key words. A unit says what we measure in. Metric units are based on 10, 100 and 1000, so converting means multiplying or dividing by powers of 10.

Method. To change units, use the conversion fact. Change to a smaller unit: multiply. Change to a bigger unit: divide.

1. Write down the conversion fact. We need to know how many of the smaller unit make one of the bigger unit.
   1 litre = 1000 ml
2. Decide: ml to litre means changing to a bigger unit, so divide. A bigger unit means you need fewer of them. For example 2000 ml is only 2 litres. So we divide by 1000.
   2500 ml ÷ 1000
3. Calculate. Dividing by 10, 100 or 1000 moves each digit to the right.
   2500 ÷ 1000 = 2.5
4. Write the answer with its unit. Always put the new unit in the answer.
   2500 ml = 2.5 litres

Check. Convert back: 2.5 × 1000 = 2500. ✓

Watch out. Check the direction: there are always more of the smaller unit. If your answer for centimetres is smaller than the number of metres, you divided when you should have multiplied.

Key words. A unit says what we measure in. Metric units are based on 10, 100 and 1000, so converting means multiplying or dividing by powers of 10.

Method. To change units, use the conversion fact. Change to a smaller unit: multiply. Change to a bigger unit: divide.

1. Write down the conversion fact. We need to know how many of the smaller unit make one of the bigger unit.
   1 tonne = 1000 kg
2. Decide: tonne to kg means changing to a smaller unit, so multiply. A smaller unit means you need more of them. For example 2 tonnes is 2000 kg. So we multiply by 1000.
   4.2 tonnes × 1000
3. Calculate.
   4.2 × 1000 = 4200
4. Write the answer with its unit. Always put the new unit in the answer.
   4.2 tonnes = 4200 kg

Check. Convert back: 4200 ÷ 1000 = 4.2. ✓

Watch out. Check the direction: there are always more of the smaller unit. If your answer for centimetres is smaller than the number of metres, you divided when you should have multiplied.

Key words. A unit says what we measure in. Metric units are based on 10, 100 and 1000, so converting means multiplying or dividing by powers of 10.

Method. To change units, use the conversion fact. Change to a smaller unit: multiply. Change to a bigger unit: divide.

1. Write down the conversion fact. We need to know how many of the smaller unit make one of the bigger unit.
   1 kg = 1000 g
2. Decide: g to kg means changing to a bigger unit, so divide. A bigger unit means you need fewer of them. For example 2000 g is only 2 kg. So we divide by 1000.
   650 g ÷ 1000
3. Calculate. Dividing by 10, 100 or 1000 moves each digit to the right.
   650 ÷ 1000 = 0.65
4. Write the answer with its unit. Always put the new unit in the answer.
   650 g = 0.65 kg

Check. Convert back: 0.65 × 1000 = 650. ✓

Watch out. Check the direction: there are always more of the smaller unit. If your answer for centimetres is smaller than the number of metres, you divided when you should have multiplied.

Method. Count the whole centimetres, then the small marks (each is 1 mm).

1. Find the value of one small mark. There are 10 small marks between each pair of centimetre marks, so each is 1 mm.
   1 small mark = 1 mm
2. Read the length. The pencil reaches 7 whole centimetres and 3 more small marks.
   7 cm = 70 mm, then 70 + 3 = 73 mm

Check. 73 mm is between 7 cm and 8 cm. ✓

Method. To change mm to cm, divide by 10.

1. Use the fact 1 cm = 10 mm. A centimetre is bigger than a millimetre, so there are fewer of them.
   73 ÷ 10
2. Divide. Move the digits one place to the right.
   73 ÷ 10 = 7.3 cm

Check. 7.3 × 10 = 73. ✓

Method. Take two labelled marks, find the difference, and divide by the number of gaps.

1. Pick two labelled marks. The marks 40 and 50 are labelled.
   50 − 40 = 10 ml
2. Count the gaps between them. There are 2 small gaps between 40 and 50.
   10 ÷ 2 = 5 ml

Check. 2 gaps × 5 ml = 10 ml. ✓

Method. Read the level of the liquid against the scale.

1. Find the labelled mark just below the level. The liquid is above the 40 mark and below the 50 mark.
   40 ml
2. Count the small divisions above it. The top of the liquid is one small division (5 ml) above the 40 mark.
   40 + 5 = 45 ml

Check. The level is one small division above 40 ml, plus another: 40 + 5 = 45. ✓

Method. The 24-hour clock counts the hours from 00 to 23, so afternoon times are the 12-hour time plus 12 hours.

1. Decide if the time is am or pm. am is from midnight to noon. pm is from noon to midnight.
   7:05 pm
2. Find the 24-hour hour. Afternoon and evening times (pm) have 12 added to the hour, except for 12 noon, which stays as 12.
   7 + 12 = 19
3. Write four digits: hours then minutes. The 24-hour clock always uses two digits for the hours and two digits for the minutes.
   19:05

Check. Back again: 19:05 on a 12-hour clock is 7:05 pm. ✓

Watch out. Do not add 12 to a morning time, and do not add 12 to 12 noon.

Method. The 24-hour clock counts the hours from 00 to 23, so afternoon times are the 12-hour time plus 12 hours.

1. Decide if the time is am or pm. am is from midnight to noon. pm is from noon to midnight.
   12:30 am
2. Find the 24-hour hour. 12:xx am is just after midnight, so the hour is 00.
   12 = 0
3. Write four digits: hours then minutes. The 24-hour clock always uses two digits for the hours and two digits for the minutes.
   00:30

Check. Back again: 00:30 on a 12-hour clock is 12:30 am. ✓

Watch out. Do not add 12 to a morning time, and do not add 12 to 12 noon.

Method. The 24-hour clock counts the hours from 00 to 23, so afternoon times are the 12-hour time plus 12 hours.

1. Decide if the time is am or pm. am is from midnight to noon. pm is from noon to midnight.
   9:45 am
2. Find the 24-hour hour. Morning times (am) stay the same, except that 12 midnight is 00.
   9 = 9
3. Write four digits: hours then minutes. The 24-hour clock always uses two digits for the hours and two digits for the minutes.
   09:45

Check. Back again: 09:45 on a 12-hour clock is 9:45 am. ✓

Watch out. Do not add 12 to a morning time, and do not add 12 to 12 noon.

Method. The 24-hour clock counts the hours from 00 to 23, so afternoon times are the 12-hour time plus 12 hours.

1. Decide if the time is am or pm. am is from midnight to noon. pm is from noon to midnight.
   11:20 pm
2. Find the 24-hour hour. Afternoon and evening times (pm) have 12 added to the hour, except for 12 noon, which stays as 12.
   11 + 12 = 23
3. Write four digits: hours then minutes. The 24-hour clock always uses two digits for the hours and two digits for the minutes.
   23:20

Check. Back again: 23:20 on a 12-hour clock is 11:20 pm. ✓

Watch out. Do not add 12 to a morning time, and do not add 12 to 12 noon.

Method. Hours 13 to 23 are pm; subtract 12 from them. Hours 1 to 11 are am; 12 is noon; 00 is midnight.

1. Look at the hour. The 24-hour clock counts 00 to 23. The first 12 hours of the day are am and the second 12 hours are pm.
   15:40: hour = 15
2. Change the hour to a 12-hour clock hour. Times from 13:00 onwards are pm. Take away 12 from the hour.
   15 − 12 = 3 pm
3. Write the time. Keep the minutes and add am or pm.
   3:40 pm

Check. Forward again: 3:40 pm is 15:40 on the 24-hour clock. ✓

Method. Hours 13 to 23 are pm; subtract 12 from them. Hours 1 to 11 are am; 12 is noon; 00 is midnight.

1. Look at the hour. The 24-hour clock counts 00 to 23. The first 12 hours of the day are am and the second 12 hours are pm.
   00:10: hour = 0
2. Change the hour to a 12-hour clock hour. The hours 00:xx are just after midnight, which is 12 am.
   00 → 12 am
3. Write the time. Keep the minutes and add am or pm.
   12:10 am

Check. Forward again: 12:10 am is 00:10 on the 24-hour clock. ✓

Method. Hours 13 to 23 are pm; subtract 12 from them. Hours 1 to 11 are am; 12 is noon; 00 is midnight.

1. Look at the hour. The 24-hour clock counts 00 to 23. The first 12 hours of the day are am and the second 12 hours are pm.
   12:25: hour = 12
2. Change the hour to a 12-hour clock hour. The hours 12:xx are just after noon, so they are pm and the hour stays 12.
   12 pm
3. Write the time. Keep the minutes and add am or pm.
   12:25 pm

Check. Forward again: 12:25 pm is 12:25 on the 24-hour clock. ✓

Method. Hours 13 to 23 are pm; subtract 12 from them. Hours 1 to 11 are am; 12 is noon; 00 is midnight.

1. Look at the hour. The 24-hour clock counts 00 to 23. The first 12 hours of the day are am and the second 12 hours are pm.
   21:05: hour = 21
2. Change the hour to a 12-hour clock hour. Times from 13:00 onwards are pm. Take away 12 from the hour.
   21 − 12 = 9 pm
3. Write the time. Keep the minutes and add am or pm.
   9:05 pm

Check. Forward again: 9:05 pm is 21:05 on the 24-hour clock. ✓

Method. Count on in stages: to the next hour, then whole hours, then the remaining minutes. Then add up.

1. Count on from 09:45 to the next whole hour, 10:00. Counting to the next hour gives an easy place to start. 60 minutes make an hour, so subtract the minutes from 60.
   60 − 45 = 15 minutes
2. Count the whole hours from 10:00 to 13:00.
   3 hours
3. Count on from 13:00 to 13:20.
   20 minutes
4. Add the parts together. Total the hours, then total the minutes. If the minutes reach 60 or more, change 60 minutes into 1 hour.
   15 minutes + 3 hours + 20 minutes
   Minutes: 15 + 20 = 35
   Total: 3 hours 35 minutes

Check. Add the journey time to the start: 09:45 + 3 hours 35 min = 13:20. ✓

Watch out. There are 60 minutes in an hour, not 100. So 10:40 to 11:10 is 30 minutes, not 70.

Method. Count on in stages: to the next hour, then whole hours, then the remaining minutes. Then add up.

1. Count on in whole hours from the start time. Hours are easy to count, so count them first.
   10:00 to 12:00 is 2 hours
2. Count on the remaining minutes.
   12:00 to 12:35 is 35 minutes
3. Add the parts together. Total the hours, then total the minutes. If the minutes reach 60 or more, change 60 minutes into 1 hour.
   2 hours + 35 minutes
   Total: 2 hours 35 minutes

Check. Add the journey time to the start: 10:00 + 2 hours 35 min = 12:35. ✓

Watch out. There are 60 minutes in an hour, not 100. So 10:40 to 11:10 is 30 minutes, not 70.

Method. Count on in stages: to the next hour, then whole hours, then the remaining minutes. Then add up.

1. Count on from 14:50 to the next whole hour, 15:00. Counting to the next hour gives an easy place to start. 60 minutes make an hour, so subtract the minutes from 60.
   60 − 50 = 10 minutes
2. Count the whole hours from 15:00 to 17:00.
   2 hours
3. Count on from 17:00 to 17:15.
   15 minutes
4. Add the parts together. Total the hours, then total the minutes. If the minutes reach 60 or more, change 60 minutes into 1 hour.
   10 minutes + 2 hours + 15 minutes
   Minutes: 10 + 15 = 25
   Total: 2 hours 25 minutes

Check. Add the journey time to the start: 14:50 + 2 hours 25 min = 17:15. ✓

Watch out. There are 60 minutes in an hour, not 100. So 10:40 to 11:10 is 30 minutes, not 70.

Method. Count on in stages: to the next hour, then whole hours, then the remaining minutes. Then add up.

1. Count on from 06:35 to the next whole hour, 07:00. Counting to the next hour gives an easy place to start. 60 minutes make an hour, so subtract the minutes from 60.
   60 − 35 = 25 minutes
2. Count the whole hours from 07:00 to 11:00.
   4 hours
3. Count on from 11:00 to 11:10.
   10 minutes
4. Add the parts together. Total the hours, then total the minutes. If the minutes reach 60 or more, change 60 minutes into 1 hour.
   25 minutes + 4 hours + 10 minutes
   Minutes: 25 + 10 = 35
   Total: 4 hours 35 minutes

Check. Add the journey time to the start: 06:35 + 4 hours 35 min = 11:10. ✓

Watch out. There are 60 minutes in an hour, not 100. So 10:40 to 11:10 is 30 minutes, not 70.

Method. Add the hours, then the minutes. If the minutes reach 60, change them into an hour.

1. Add the hours. Hours go straight onto the clock hours.
   08:50 + 2 hours = 10:50
2. Add the minutes. Add the minutes to the minutes on the clock. If you get 60 or more, take away 60 and add 1 to the hour.
   50 + 25 = 75 minutes = 1 hour 15 minutes
3. Write the new time. Use two digits for hours and minutes on the 24-hour clock.
   11:15

Check. Count back: 11:15 take away 2 h 25 min is 08:50. ✓

Watch out. Minutes go up to 59, then it becomes the next hour. 14:50 + 25 minutes is 15:15, not 14:75.

Method. Add the hours, then the minutes. If the minutes reach 60, change them into an hour.

1. Add the hours. Hours go straight onto the clock hours.
   14:35 + 1 hour = 15:35
2. Add the minutes. Add the minutes to the minutes on the clock. If you get 60 or more, take away 60 and add 1 to the hour.
   35 + 50 = 85 minutes = 1 hour 25 minutes
3. Write the new time. Use two digits for hours and minutes on the 24-hour clock.
   16:25

Check. Count back: 16:25 take away 1 h 50 min is 14:35. ✓

Watch out. Minutes go up to 59, then it becomes the next hour. 14:50 + 25 minutes is 15:15, not 14:75.

Method. Add the hours, then the minutes. If the minutes reach 60, change them into an hour.

1. Add the hours. Hours go straight onto the clock hours.
   22:50 + 2 hours = 00:50 (next day)
2. Add the minutes. Add the minutes to the minutes on the clock. If you get 60 or more, take away 60 and add 1 to the hour.
   50 + 25 = 75 minutes = 1 hour 15 minutes
3. Write the new time. Use two digits for hours and minutes on the 24-hour clock. The time has gone past midnight, so it is on the next day.
   01:15 the next day

Check. Count back: 01:15 take away 2 h 25 min is 22:50. ✓

Watch out. Minutes go up to 59, then it becomes the next hour. 14:50 + 25 minutes is 15:15, not 14:75.

Key words. A unit says what we measure in. Metric units are based on 10, 100 and 1000, so converting means multiplying or dividing by powers of 10.

Method. To change units, use the conversion fact. Change to a smaller unit: multiply. Change to a bigger unit: divide.

1. Write down the conversion fact. We need to know how many of the smaller unit make one of the bigger unit.
   1 hour = 60 min
2. Decide: hour to min means changing to a smaller unit, so multiply. A smaller unit means you need more of them. For example 2 hours is 120 min. So we multiply by 60.
   3 hours × 60
3. Calculate.
   3 × 60 = 180
4. Write the answer with its unit. Always put the new unit in the answer.
   3 hours = 180 min

Check. Convert back: 180 ÷ 60 = 3. ✓

Watch out. Check the direction: there are always more of the smaller unit. If your answer for centimetres is smaller than the number of metres, you divided when you should have multiplied.

Key words. A unit says what we measure in. Metric units are based on 10, 100 and 1000, so converting means multiplying or dividing by powers of 10.

Method. To change units, use the conversion fact. Change to a smaller unit: multiply. Change to a bigger unit: divide.

1. Write down the conversion fact. We need to know how many of the smaller unit make one of the bigger unit.
   1 min = 60 s
2. Decide: min to s means changing to a smaller unit, so multiply. A smaller unit means you need more of them. For example 2 min is 120 s. So we multiply by 60.
   5 min × 60
3. Calculate.
   5 × 60 = 300
4. Write the answer with its unit. Always put the new unit in the answer.
   5 min = 300 s

Check. Convert back: 300 ÷ 60 = 5. ✓

Watch out. Check the direction: there are always more of the smaller unit. If your answer for centimetres is smaller than the number of metres, you divided when you should have multiplied.

Key words. A unit says what we measure in. Metric units are based on 10, 100 and 1000, so converting means multiplying or dividing by powers of 10.

Method. To change units, use the conversion fact. Change to a smaller unit: multiply. Change to a bigger unit: divide.

1. Write down the conversion fact. We need to know how many of the smaller unit make one of the bigger unit.
   1 week = 7 days
2. Decide: week to day means changing to a smaller unit, so multiply. A smaller unit means you need more of them. For example 2 weeks is 14 days. So we multiply by 7.
   4 weeks × 7
3. Calculate.
   4 × 7 = 28
4. Write the answer with its unit. Always put the new unit in the answer.
   4 weeks = 28 days

Check. Convert back: 28 ÷ 7 = 4. ✓

Watch out. Check the direction: there are always more of the smaller unit. If your answer for centimetres is smaller than the number of metres, you divided when you should have multiplied.

Key words. A unit says what we measure in. Metric units are based on 10, 100 and 1000, so converting means multiplying or dividing by powers of 10.

Method. To change units, use the conversion fact. Change to a smaller unit: multiply. Change to a bigger unit: divide.

1. Write down the conversion fact. We need to know how many of the smaller unit make one of the bigger unit.
   1 day = 24 hours
2. Decide: day to hour means changing to a smaller unit, so multiply. A smaller unit means you need more of them. For example 2 days is 48 hours. So we multiply by 24.
   2 days × 24
3. Calculate.
   2 × 24 = 48
4. Write the answer with its unit. Always put the new unit in the answer.
   2 days = 48 hours

Check. Convert back: 48 ÷ 24 = 2. ✓

Watch out. Check the direction: there are always more of the smaller unit. If your answer for centimetres is smaller than the number of metres, you divided when you should have multiplied.

Key words. The sum or total is the answer to an addition. Carry means move the tens digit of a column total to the next column on the left.

Method. Add using columns. Line up the place values, add from the right, and carry when a column reaches 10 or more.

1. Line up the numbers in columns. Digits can only be added when they are worth the same, so units go under units, tens under tens, and decimal points under decimal points. Fill any gaps with zeros.
   1.85 3.60 + 2.45 ------
2. Add the columns, starting on the right. We start with the smallest column. If a column adds up to 10 or more, we write the units digit and carry the tens digit to the next column.
   Hundredths: 5 + 0 + 5 = 10. Write 0 and carry 1 into the tenths column.
   Tenths: 8 + 6 + 4 + 1 (carried) = 19. Write 9 and carry 1 into the units column.
   Units: 1 + 3 + 2 + 1 (carried) = 7. Write 7.
3. Put the decimal point in the answer. The point goes directly under the other decimal points.
   1.85 3.60 + 2.45 ------ 7.90 1 1
   1.85 + 3.6 + 2.45 = 7.9

Check. Check with an inverse (opposite) operation: 7.9 − 2.45 = 5.45 = 5.45, which is 1.85 + 3.6. ✓

Watch out. Line up the decimal points, not the right-hand ends of the numbers. 5.2 + 0.37 needs 5.20 + 0.37.

Key words. The difference is the answer to a subtraction. Exchange (or borrowing) means taking 1 from a column and putting 10 into the column on its right.

Method. Subtract using columns. Line up the place values, subtract from the right, and exchange when the top digit is too small.

1. Line up the numbers in columns, with the bigger number on top. Digits can only be subtracted when they are worth the same: units under units, tens under tens, decimal points under decimal points. Fill gaps with zeros.
   10.0 − 7.9 ------
2. Subtract each column, starting on the right. If the top digit is smaller than the digit below it, we exchange (borrow): take 1 from the column on the left and add it to this column as 10.
   Tenths: 0 is smaller than 9, so we must exchange. The units column is 0, so there is nothing to take there. Go left to the tens column. Take 1 ten (1 becomes 0) and exchange it for 10 units. Take 1 of those units (leaving 9) and exchange it for 10 tenths. 0 becomes 10. Now 10 − 9 = 1.
   Units: 9 − 7 = 2.
   Tens: 0 − 0 = 0.
3. Write the answer. Put the decimal point in line with the others.
   10.0 − 7.9 ------ 02.1
   10 − 7.9 = 2.1

Check. Check with the inverse (opposite) operation, addition: 2.1 + 7.9 = 10. ✓

Watch out. Always subtract the smaller number from the bigger in each column only after exchanging. Never take the top digit from the bottom one.

Method. A decimal part of an hour is a fraction of 60 minutes: multiply the decimal part by 60.

1. Split the number into whole hours and a decimal part. The whole number is whole hours. The decimal is a part of one hour.
   2.25 hours = 2 hours + 0.25 hours
2. Change the decimal part of an hour into minutes. 1 hour is 60 minutes, so multiply the decimal by 60.
   0.25 × 60 = 15 minutes
3. Write the answer.
   2 hours 15 minutes

Check. 2 + 15 ÷ 60 = 2 + 0.25 = 2.25. ✓

Watch out. 1.5 hours is 1 hour 30 minutes, not 1 hour 50 minutes. Time is not in tens.

Method. A decimal part of an hour is a fraction of 60 minutes: multiply the decimal part by 60.

1. Split the number into whole hours and a decimal part. The whole number is whole hours. The decimal is a part of one hour.
   3.5 hours = 3 hours + 0.5 hours
2. Change the decimal part of an hour into minutes. 1 hour is 60 minutes, so multiply the decimal by 60.
   0.5 × 60 = 30 minutes
3. Write the answer.
   3 hours 30 minutes

Check. 3 + 30 ÷ 60 = 3 + 0.5 = 3.5. ✓

Watch out. 1.5 hours is 1 hour 30 minutes, not 1 hour 50 minutes. Time is not in tens.

Method. A decimal part of an hour is a fraction of 60 minutes: multiply the decimal part by 60.

1. Change the decimal part of an hour into minutes. 1 hour is 60 minutes, so multiply the decimal by 60.
   0.2 × 60 = 12 minutes
2. Write the answer.
   12 minutes

Check. 0 + 12 ÷ 60 = 0 + 0.2 = 0.2. ✓

Watch out. 1.5 hours is 1 hour 30 minutes, not 1 hour 50 minutes. Time is not in tens.

Method. Divide the minutes by 60 to get hours.

1. Remember there are 60 minutes in 1 hour. To change minutes into hours we divide by 60, because each hour is a bigger unit.
   45 minutes = 45 ÷ 60 hours
2. Divide. Simplify the fraction or divide.
   45 ÷ 60 = 0.75

Check. 0.75 × 60 = 45 minutes. ✓