Step-by-step Maths Level 5: Adding and subtracting measures
Part of the Step-by-step Maths Level 5 metric length, mass and capacity chapter. Chapter overview · whole chapter on one page
Adding and subtracting measures
To add or subtract mixed units, change both measures to the smaller unit first. Then calculate, and change the answer back.
For example, 2 m 35 cm + 1 m 80 cm = 235 cm + 180 cm = 415 cm = 4 m 15 cm.
Key ideas
- Change both measures to the same unit first.
- Add or subtract the smaller unit.
- Change the answer back into mixed units.
Method. Change both measures to the same unit, cm, then add, then change back.
- Change both to cm. 1 m = 100 cm.2 m 35 cm = 235 cm, and 1 m 80 cm = 180 cm
- Add the cm. Work with the same unit.235 + 180 = 415 cm
- Change back to m and cm. Share the cm into groups of 100.415 = 4 m and 15 cm
- Write the answer. Give the answer in mixed units, as the question was.4 m 15 cm
Check. Check: 4 m 15 cm - 1 m 80 cm gives 2 m 35 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, g, then subtract, then change back.
- Change both to g. 1 kg = 1,000 g.3 kg 250 g = 3,250 g, and 1 kg 600 g = 1,600 g
- Subtract the g. Work with the same unit.3,250 - 1,600 = 1,650 g
- Change back to kg and g. Share the g into groups of 1,000.1,650 = 1 kg and 650 g
- Write the answer. Give the answer in mixed units, as the question was.1 kg 650 g
Check. Check: 1 kg 650 g + 3 kg 250 g gives 1 kg 600 g again.
Watch out. Keep the unit with each number. A total of 1,000 g is 1 kg.
Method. Change both measures to the same unit, ml, then add, then change back.
- Change both to ml. 1 l = 1,000 ml.1 l 500 ml = 1,500 ml, and 750 ml = 750 ml
- Add the ml. Work with the same unit.1,500 + 750 = 2,250 ml
- Change back to l and ml. Share the ml into groups of 1,000.2,250 = 2 l and 250 ml
- Write the answer. Give the answer in mixed units, as the question was.2 l 250 ml
Check. Check: 2 l 250 ml - 750 ml gives 1 l 500 ml again.
Watch out. Keep the unit with each number. A total of 1,000 ml is 1 l.
Watch out
Watch out. Do not add the metres and the centimetres separately as if they were the same unit. Change to one unit first.
Exam tip
Grown-up tip. Ask: “How many centimetres is that altogether? Now how many metres and centimetres?”
Exercise 8C Practice: adding and subtracting measures
Non-calculatorMethod. Change both measures to the same unit, cm, then subtract, then change back.
- Change both to cm. 1 m = 100 cm.3 m 20 cm = 320 cm, and 2 m 66 cm = 266 cm
- Subtract the cm. Work with the same unit.320 - 266 = 54 cm
- Change back to m and cm. Share the cm into groups of 100.54 = 0 m and 54 cm
- Write the answer. Give the answer in mixed units, as the question was.54 cm
Check. Check: 54 cm + 3 m 20 cm gives 2 m 66 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, g, then add, then change back.
- Change both to g. 1 kg = 1,000 g.2 kg 203 g = 2,203 g, and 1 kg 830 g = 1,830 g
- Add the g. Work with the same unit.2,203 + 1,830 = 4,033 g
- Change back to kg and g. Share the g into groups of 1,000.4,033 = 4 kg and 33 g
- Write the answer. Give the answer in mixed units, as the question was.4 kg 33 g
Check. Check: 4 kg 33 g - 1 kg 830 g gives 2 kg 203 g again.
Watch out. Keep the unit with each number. A total of 1,000 g is 1 kg.
Method. Change both measures to the same unit, g, then add, then change back.
- Change both to g. 1 kg = 1,000 g.4 kg 766 g = 4,766 g, and 2 kg 201 g = 2,201 g
- Add the g. Work with the same unit.4,766 + 2,201 = 6,967 g
- Change back to kg and g. Share the g into groups of 1,000.6,967 = 6 kg and 967 g
- Write the answer. Give the answer in mixed units, as the question was.6 kg 967 g
Check. Check: 6 kg 967 g - 2 kg 201 g gives 4 kg 766 g again.
Watch out. Keep the unit with each number. A total of 1,000 g is 1 kg.
Method. Change both measures to the same unit, mm, then subtract, then change back.
- Change both to mm. 1 cm = 10 mm.4 cm 4 mm = 44 mm, and 2 cm 6 mm = 26 mm
- Subtract the mm. Work with the same unit.44 - 26 = 18 mm
- Change back to cm and mm. Share the mm into groups of 10.18 = 1 cm and 8 mm
- Write the answer. Give the answer in mixed units, as the question was.1 cm 8 mm
Check. Check: 1 cm 8 mm + 4 cm 4 mm gives 2 cm 6 mm again.
Watch out. Keep the unit with each number. A total of 10 mm is 1 cm.
Method. Change both measures to the same unit, cm, then subtract, then change back.
- Change both to cm. 1 m = 100 cm.4 m 37 cm = 437 cm, and 2 m 18 cm = 218 cm
- Subtract the cm. Work with the same unit.437 - 218 = 219 cm
- Change back to m and cm. Share the cm into groups of 100.219 = 2 m and 19 cm
- Write the answer. Give the answer in mixed units, as the question was.2 m 19 cm
Check. Check: 2 m 19 cm + 4 m 37 cm gives 2 m 18 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, g, then add, then change back.
- Change both to g. 1 kg = 1,000 g.2 kg 412 g = 2,412 g, and 298 g = 298 g
- Add the g. Work with the same unit.2,412 + 298 = 2,710 g
- Change back to kg and g. Share the g into groups of 1,000.2,710 = 2 kg and 710 g
- Write the answer. Give the answer in mixed units, as the question was.2 kg 710 g
Check. Check: 2 kg 710 g - 298 g gives 2 kg 412 g again.
Watch out. Keep the unit with each number. A total of 1,000 g is 1 kg.
Method. Change both measures to the same unit, mm, then add, then change back.
- Change both to mm. 1 cm = 10 mm.3 cm 8 mm = 38 mm, and 1 cm 5 mm = 15 mm
- Add the mm. Work with the same unit.38 + 15 = 53 mm
- Change back to cm and mm. Share the mm into groups of 10.53 = 5 cm and 3 mm
- Write the answer. Give the answer in mixed units, as the question was.5 cm 3 mm
Check. Check: 5 cm 3 mm - 1 cm 5 mm gives 3 cm 8 mm again.
Watch out. Keep the unit with each number. A total of 10 mm is 1 cm.
Method. Change both measures to the same unit, cm, then subtract, then change back.
- Change both to cm. 1 m = 100 cm.2 m 71 cm = 271 cm, and 1 cm = 1 cm
- Subtract the cm. Work with the same unit.271 - 1 = 270 cm
- Change back to m and cm. Share the cm into groups of 100.270 = 2 m and 70 cm
- Write the answer. Give the answer in mixed units, as the question was.2 m 70 cm
Check. Check: 2 m 70 cm + 2 m 71 cm gives 1 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, mm, then subtract, then change back.
- Change both to mm. 1 cm = 10 mm.4 cm 2 mm = 42 mm, and 2 cm 4 mm = 24 mm
- Subtract the mm. Work with the same unit.42 - 24 = 18 mm
- Change back to cm and mm. Share the mm into groups of 10.18 = 1 cm and 8 mm
- Write the answer. Give the answer in mixed units, as the question was.1 cm 8 mm
Check. Check: 1 cm 8 mm + 4 cm 2 mm gives 2 cm 4 mm again.
Watch out. Keep the unit with each number. A total of 10 mm is 1 cm.
Method. Change both measures to the same unit, g, then subtract, then change back.
- Change both to g. 1 kg = 1,000 g.3 kg 93 g = 3,093 g, and 1 kg 363 g = 1,363 g
- Subtract the g. Work with the same unit.3,093 - 1,363 = 1,730 g
- Change back to kg and g. Share the g into groups of 1,000.1,730 = 1 kg and 730 g
- Write the answer. Give the answer in mixed units, as the question was.1 kg 730 g
Check. Check: 1 kg 730 g + 3 kg 93 g gives 1 kg 363 g again.
Watch out. Keep the unit with each number. A total of 1,000 g is 1 kg.
Method. Change both measures to the same unit, mm, then add, then change back.
- Change both to mm. 1 cm = 10 mm.2 cm 8 mm = 28 mm, and 5 mm = 5 mm
- Add the mm. Work with the same unit.28 + 5 = 33 mm
- Change back to cm and mm. Share the mm into groups of 10.33 = 3 cm and 3 mm
- Write the answer. Give the answer in mixed units, as the question was.3 cm 3 mm
Check. Check: 3 cm 3 mm - 5 mm gives 2 cm 8 mm again.
Watch out. Keep the unit with each number. A total of 10 mm is 1 cm.
Method. Change both measures to the same unit, mm, then subtract, then change back.
- Change both to mm. 1 cm = 10 mm.3 cm 4 mm = 34 mm, and 4 mm = 4 mm
- Subtract the mm. Work with the same unit.34 - 4 = 30 mm
- Change back to cm and mm. Share the mm into groups of 10.30 = 3 cm and 0 mm
- Write the answer. Give the answer in mixed units, as the question was.3 cm
Check. Check: 3 cm + 3 cm 4 mm gives 4 mm again.
Watch out. Keep the unit with each number. A total of 10 mm is 1 cm.
Method. Change both measures to the same unit, ml, then add, then change back.
- Change both to ml. 1 l = 1,000 ml.3 l 728 ml = 3,728 ml, and 944 ml = 944 ml
- Add the ml. Work with the same unit.3,728 + 944 = 4,672 ml
- Change back to l and ml. Share the ml into groups of 1,000.4,672 = 4 l and 672 ml
- Write the answer. Give the answer in mixed units, as the question was.4 l 672 ml
Check. Check: 4 l 672 ml - 944 ml gives 3 l 728 ml again.
Watch out. Keep the unit with each number. A total of 1,000 ml is 1 l.
Method. Change both measures to the same unit, g, then subtract, then change back.
- Change both to g. 1 kg = 1,000 g.4 kg 245 g = 4,245 g, and 2 kg 783 g = 2,783 g
- Subtract the g. Work with the same unit.4,245 - 2,783 = 1,462 g
- Change back to kg and g. Share the g into groups of 1,000.1,462 = 1 kg and 462 g
- Write the answer. Give the answer in mixed units, as the question was.1 kg 462 g
Check. Check: 1 kg 462 g + 4 kg 245 g gives 2 kg 783 g again.
Watch out. Keep the unit with each number. A total of 1,000 g is 1 kg.
Method. Change both measures to the same unit, g, then subtract, then change back.
- Change both to g. 1 kg = 1,000 g.3 kg 834 g = 3,834 g, and 1 kg 781 g = 1,781 g
- Subtract the g. Work with the same unit.3,834 - 1,781 = 2,053 g
- Change back to kg and g. Share the g into groups of 1,000.2,053 = 2 kg and 53 g
- Write the answer. Give the answer in mixed units, as the question was.2 kg 53 g
Check. Check: 2 kg 53 g + 3 kg 834 g gives 1 kg 781 g again.
Watch out. Keep the unit with each number. A total of 1,000 g is 1 kg.
Method. Change both measures to the same unit, g, then subtract, then change back.
- Change both to g. 1 kg = 1,000 g.2 kg 351 g = 2,351 g, and 562 g = 562 g
- Subtract the g. Work with the same unit.2,351 - 562 = 1,789 g
- Change back to kg and g. Share the g into groups of 1,000.1,789 = 1 kg and 789 g
- Write the answer. Give the answer in mixed units, as the question was.1 kg 789 g
Check. Check: 1 kg 789 g + 2 kg 351 g gives 562 g again.
Watch out. Keep the unit with each number. A total of 1,000 g is 1 kg.