Step-by-step Maths Level 5 Metric length, mass and capacity: check-up and practice test questions

Method. Divide by 1,000 to find the whole l; the remainder is the ml.

1. Use the rule. 1 l is 1,000 ml.
   1 l = 1,000 ml
2. Share 5,890 ml into groups of 1,000. Each group is one l.
   5,890 ÷ 1,000 = 5 r 890
3. Write the answer. 5 whole l and the ml left over.
   5 l 890 ml

Check. Check: 5 × 1,000 + 890 = 5,890.

Watch out. Use a space between the two parts, and the unit after each: 5 l 890 ml.

Method. Divide by 10 to find the whole cm; the remainder is the mm.

1. Use the rule. 1 cm is 10 mm.
   1 cm = 10 mm
2. Share 134 mm into groups of 10. Each group is one cm.
   134 ÷ 10 = 13 r 4
3. Write the answer. 13 whole cm and the mm left over.
   13 cm 4 mm

Check. Check: 13 × 10 + 4 = 134.

Watch out. Use a space between the two parts, and the unit after each: 13 cm 4 mm.

Method. Change both measures to the same unit, mm, then add, then change back.

1. Change both to mm. 1 cm = 10 mm.
   1 cm 3 mm = 13 mm, and 2 mm = 2 mm
2. Add the mm. Work with the same unit.
   13 + 2 = 15 mm
3. Change back to cm and mm. Share the mm into groups of 10.
   15 = 1 cm and 5 mm
4. Write the answer. Give the answer in mixed units, as the question was.
   1 cm 5 mm

Check. Check: 1 cm 5 mm - 2 mm gives 1 cm 3 mm again.

Watch out. Keep the unit with each number. A total of 10 mm is 1 cm.

Method. Multiply the measure by the number of items, then change to mixed units.

1. Work out the total in the smallest unit. Each one is 2,658 g.
   2,658 g × 3 = 7,974 g
2. Change back to kg and g. Share the g into groups of 1,000.
   7,974 g = 7 kg 974 g
3. Write the answer. Give the total in mixed units.
   7 kg 974 g

Check. Check: 7,974 ÷ 3 = 2,658.

Watch out. Multiply in the small unit, then change back at the end.

Method. Change both measures to the same unit, g, then subtract, then change back.

1. Change both to g. 1 kg = 1,000 g.
   3 kg 235 g = 3,235 g, and 2 kg 718 g = 2,718 g
2. Subtract the g. Work with the same unit.
   3,235 - 2,718 = 517 g
3. Change back to kg and g. Share the g into groups of 1,000.
   517 = 0 kg and 517 g
4. Write the answer. Give the answer in mixed units, as the question was.
   517 g

Check. Check: 517 g + 3 kg 235 g gives 2 kg 718 g again.

Watch out. Keep the unit with each number. A total of 1,000 g is 1 kg.

Method. Multiply the measure by the number of items, then change to mixed units.

1. Work out the total in the smallest unit. Each one is 1,458 ml.
   1,458 ml × 2 = 2,916 ml
2. Change back to l and ml. Share the ml into groups of 1,000.
   2,916 ml = 2 l 916 ml
3. Write the answer. Give the total in mixed units.
   2 l 916 ml

Check. Check: 2,916 ÷ 2 = 1,458.

Watch out. Multiply in the small unit, then change back at the end.

Method. Divide by 1,000 to find the whole kg; the remainder is the g.

1. Use the rule. 1 kg is 1,000 g.
   1 kg = 1,000 g
2. Share 15,524 g into groups of 1,000. Each group is one kg.
   15,524 ÷ 1,000 = 15 r 524
3. Write the answer. 15 whole kg and the g left over.
   15 kg 524 g

Check. Check: 15 × 1,000 + 524 = 15,524.

Watch out. Use a space between the two parts, and the unit after each: 15 kg 524 g.

Method. Divide by 1,000 to find the whole kg; the remainder is the g.

1. Use the rule. 1 kg is 1,000 g.
   1 kg = 1,000 g
2. Share 3,329 g into groups of 1,000. Each group is one kg.
   3,329 ÷ 1,000 = 3 r 329
3. Write the answer. 3 whole kg and the g left over.
   3 kg 329 g

Check. Check: 3 × 1,000 + 329 = 3,329.

Watch out. Use a space between the two parts, and the unit after each: 3 kg 329 g.

Method. Change both measures to the same unit, cm, then add, then change back.

1. Change both to cm. 1 m = 100 cm.
   1 m 9 cm = 109 cm, and 22 cm = 22 cm
2. Add the cm. Work with the same unit.
   109 + 22 = 131 cm
3. Change back to m and cm. Share the cm into groups of 100.
   131 = 1 m and 31 cm
4. Write the answer. Give the answer in mixed units, as the question was.
   1 m 31 cm

Check. Check: 1 m 31 cm - 22 cm gives 1 m 9 cm again.

Watch out. Keep the unit with each number. A total of 100 cm is 1 m.

Method. Change both measures to the same unit, ml, then subtract, then change back.

1. Change both to ml. 1 l = 1,000 ml.
   3 l 770 ml = 3,770 ml, and 2 l 147 ml = 2,147 ml
2. Subtract the ml. Work with the same unit.
   3,770 - 2,147 = 1,623 ml
3. Change back to l and ml. Share the ml into groups of 1,000.
   1,623 = 1 l and 623 ml
4. Write the answer. Give the answer in mixed units, as the question was.
   1 l 623 ml

Check. Check: 1 l 623 ml + 3 l 770 ml gives 2 l 147 ml again.

Watch out. Keep the unit with each number. A total of 1,000 ml is 1 l.

Method. Multiply by 1,000 to change l into ml.

1. Use the rule. 1 l is 1,000 ml.
   1 l = 1,000 ml
2. Multiply the l by 1,000. Each l has 1,000 ml.
   2 × 1,000 = 2,000
3. Write the answer with the unit. The unit is ml.
   2,000 ml

Check. Check: 2,000 ÷ 1,000 = 2.

Watch out. A smaller unit gives a bigger number. Multiply by 1,000.

Method. Divide by 100 to find the whole m; the remainder is the cm.

1. Use the rule. 1 m is 100 cm.
   1 m = 100 cm
2. Share 508 cm into groups of 100. Each group is one m.
   508 ÷ 100 = 5 r 8
3. Write the answer. 5 whole m and the cm left over.
   5 m 8 cm

Check. Check: 5 × 100 + 8 = 508.

Watch out. Use a space between the two parts, and the unit after each: 5 m 8 cm.

Method. Multiply by 1,000 to change kilometres into metres.

1. Use the rule. 1 kilometre is 1,000 metres.
   1 km = 1,000 m
2. Multiply the kilometres by 1,000. Each kilometre is 1,000 metres.
   6 × 1,000 = 6,000
3. Write the answer with the unit. The unit is metres.
   6,000 m

Check. Check: 6,000 ÷ 1,000 = 6.

Watch out. Going to a smaller unit makes the number bigger. Multiply.

Method. Start at the labelled number, count the small steps, then add.

1. Find the labelled number below the arrow. Labels show the bigger steps.
   0 kg
2. Count the small steps of 2 from 0. Each small step adds 2.
   2 steps of 2 = 4 kg more
3. Add to find the reading. Add the steps to the labelled number.
   0 + 4 = 4
4. Write the reading with the unit. Give the unit of the scale.
   4 kg

Check. Check: 4 is 2 steps of 2 from zero.

Watch out. Count each small mark. Do not count the labels as steps.

Method. Choose a unit that matches the size of the thing being measured.

1. Think about the size of the thing. Towns are many kilometres apart.
2. Choose the unit that gives a sensible number. A sensible unit gives a small whole number, not a huge one.
   kilometres

Check. Check: the number of units is a sensible size for the thing.

Watch out. Use cm for small lengths, m for rooms and doors, and km for distances between towns.

Method. Change both measures to the same unit, cm, then subtract, then change back.

1. Change both to cm. 1 m = 100 cm.
   4 m 33 cm = 433 cm, and 1 m 82 cm = 182 cm
2. Subtract the cm. Work with the same unit.
   433 - 182 = 251 cm
3. Change back to m and cm. Share the cm into groups of 100.
   251 = 2 m and 51 cm
4. Write the answer. Give the answer in mixed units, as the question was.
   2 m 51 cm

Check. Check: 2 m 51 cm + 4 m 33 cm gives 1 m 82 cm again.

Watch out. Keep the unit with each number. A total of 100 cm is 1 m.

Method. Multiply the measure by the number of items, then change to mixed units.

1. Work out the total in the smallest unit. Each one is 3,330 g.
   3,330 g × 3 = 9,990 g
2. Change back to kg and g. Share the g into groups of 1,000.
   9,990 g = 9 kg 990 g
3. Write the answer. Give the total in mixed units.
   9 kg 990 g

Check. Check: 9,990 ÷ 3 = 3,330.

Watch out. Multiply in the small unit, then change back at the end.

Method. Multiply the measure by the number of items, then change to mixed units.

1. Work out the total in the smallest unit. Each one is 1,436 g.
   1,436 g × 3 = 4,308 g
2. Change back to kg and g. Share the g into groups of 1,000.
   4,308 g = 4 kg 308 g
3. Write the answer. Give the total in mixed units.
   4 kg 308 g

Check. Check: 4,308 ÷ 3 = 1,436.

Watch out. Multiply in the small unit, then change back at the end.

Method. Divide by 10 to find the whole cm; the remainder is the mm.

1. Use the rule. 1 cm is 10 mm.
   1 cm = 10 mm
2. Share 63 mm into groups of 10. Each group is one cm.
   63 ÷ 10 = 6 r 3
3. Write the answer. 6 whole cm and the mm left over.
   6 cm 3 mm

Check. Check: 6 × 10 + 3 = 63.

Watch out. Use a space between the two parts, and the unit after each: 6 cm 3 mm.

Method. Change both measures to the same unit, ml, then add, then change back.

1. Change both to ml. 1 l = 1,000 ml.
   4 l 913 ml = 4,913 ml, and 871 ml = 871 ml
2. Add the ml. Work with the same unit.
   4,913 + 871 = 5,784 ml
3. Change back to l and ml. Share the ml into groups of 1,000.
   5,784 = 5 l and 784 ml
4. Write the answer. Give the answer in mixed units, as the question was.
   5 l 784 ml

Check. Check: 5 l 784 ml - 871 ml gives 4 l 913 ml again.

Watch out. Keep the unit with each number. A total of 1,000 ml is 1 l.