Year 4: Calculating with measures
Part of the Year 4 perimeter, area and measures chapter. Chapter overview · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)
Calculating with measures
We can add, subtract, multiply and divide measures. The golden rule is: the units must be the same. We cannot add 1 m and 45 cm as 1 + 45. First change them both to centimetres: 100 cm + 45 cm = 145 cm.
Adding and subtracting. Use the column method from Chapter 2. Line up the digits, with ones under ones. Add or subtract one column at a time and carry or exchange when you need to. Write the unit in the answer.
For 346 cm + 278 cm the columns look like this.
| H | T | O | |
| 3 | 4 | 6 | |
| + | 2 | 7 | 8 |
| 6 | 2 | 4 | |
| 1 | 1 |
Changing back. If the question uses two units (like m and cm), give the answer in two units too. 425 cm is 4 m 25 cm. If it uses decimals (like 2.5 kg), give a decimal. Multiplying and dividing. Work in the smaller unit. 4 × 350 ml = 1,400 ml = 1.4 l. And 1 l ÷ 4 = 1,000 ml ÷ 4 = 250 ml.
Word problems. Read the problem slowly. Draw a bar model. Decide which calculations you need and in what order. Change the units first. Then check that the answer is sensible.
Key words. The total is all the amounts added together. The difference is how much bigger or smaller one amount is than another. To estimate is to round first to get a quick check.
Key ideas
- The units must be the same before you add or subtract.
- Change to the smaller unit. 1 m 45 cm = 145 cm.
- Use column addition and subtraction. Carry and exchange when you need to.
- Multiply and divide in the smaller unit, then change back if you need to.
- Draw a bar model for word problems.
- Check: use the inverse, or estimate by rounding.
Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.
Method. Change the measures to the same unit. Then add or subtract the numbers, and give the answer in the unit asked.
- Check the units. We can only add or subtract measures that are in the same unit.Both measures are in centimetres, so we can go straight to the calculation.
- Add the two measures. Add column by column, starting with the ones. Carry when a column makes 10 or more.346 cm + 278 cm = 624 cm
H T O 3 4 6 + 2 7 8 6 2 4 1 1 - Write the answer with its unit. A measure always needs its unit.624 cm
Check. Use the inverse: 624 − 278 = 346. ✓
Watch out. You can only add or subtract measures in the same unit. 1 m + 45 cm is not 46 of anything: change it to 145 cm first.
Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.
Method. Change the measures to the same unit. Then add or subtract the numbers, and give the answer in the unit asked.
- Change both measures to centimetres. We can only add or subtract measures that are in the same unit. Use the smaller unit so we have whole numbers.1 m 45 cm = 1 × 100 + 45 = 100 + 45 = 145 cm
2 m 80 cm = 2 × 100 + 80 = 200 + 80 = 280 cm - Add the two measures. Add column by column, starting with the ones. Carry when a column makes 10 or more.145 cm + 280 cm = 425 cm
H T O 1 4 5 + 2 8 0 4 2 5 1 - Write the answer in metres and centimetres. 100 cm = 1 m, so divide by 100 and keep the remainder.425 ÷ 100 = 4 remainder 25
425 cm = 4 m 25 cm
Check. Use the inverse: 425 − 280 = 145. ✓
Watch out. You can only add or subtract measures in the same unit. 1 m + 45 cm is not 46 of anything: change it to 145 cm first.
Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.
Method. Change the measures to the same unit. Then add or subtract the numbers, and give the answer in the unit asked.
- Change both measures to millilitres. We can only add or subtract measures that are in the same unit. Use the smaller unit so we have whole numbers.1 l = 1 × 1,000 = 1,000 ml
- Take the smaller measure away from the bigger. Subtract column by column. Exchange when a top digit is too small.1,000 ml − 350 ml = 650 ml
Th H T O 0 19 010 00 − 3 5 0 6 5 0 - Write the answer with its unit. A measure always needs its unit.650 ml
Check. Use the inverse: 650 + 350 = 1,000. ✓
Watch out. You can only add or subtract measures in the same unit. 1 m + 45 cm is not 46 of anything: change it to 145 cm first.
Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.
Method. Change the measures to the same unit. Then add or subtract the numbers, and give the answer in the unit asked.
- Change both measures to grams. We can only add or subtract measures that are in the same unit. Use the smaller unit so we have whole numbers.3 kg = 3 × 1,000 = 3,000 g
1.25 kg = 1.25 × 1,000 = 1,250 g - Take the smaller measure away from the bigger. Subtract column by column. Exchange when a top digit is too small.3,000 g − 1,250 g = 1,750 g
Th H T O 2 39 010 00 − 1 2 5 0 1 7 5 0 - Write the answer in kilograms. 1,000 g = 1 kg, so divide by 1,000.1,750 g = 1,750 ÷ 1,000 = 1.75 kg
Check. Use the inverse: 1,750 + 1,250 = 3,000. ✓
Watch out. You can only add or subtract measures in the same unit. 1 m + 45 cm is not 46 of anything: change it to 145 cm first.
Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.
Method. Multiply the measure by 4. Keep the unit.
- Multiply each part of 350 by 4. Splitting the number into hundreds, tens and ones makes the times tables easier (the distributive law).4 × 300 = 1,200
4 × 50 = 200
1,200 + 200 = 1,400 - Write the total with its unit. 1,400 ml
- Write the answer in litres. 1,000 ml = 1 l.1,400 ÷ 1,000 = 1.4 l
Check. Divide back: 1,400 ÷ 4 = 350. ✓
Watch out. The unit stays the same when you multiply by a number. 4 lots of 350 ml is still in ml.
Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.
Method. Share by dividing. Work in the small unit and keep the unit.
- Change the measure to millilitres. Work in the smaller unit so we have a whole number.1 l = 1 × 1,000 = 1,000 ml
- Divide 1,000 by 4. Use a times-table fact. 100 ÷ 4 = 25, and 1,000 is 100 × 10.100 ÷ 4 = 25
25 × 10 = 250 ml - Write the answer with its unit. A measure always needs its unit.250 ml
Check. Multiply back: 4 × 250 = 1,000. ✓
Watch out. Change to the small unit first, so you have a whole number to divide. 1 l shared between 4 is 1,000 ml ÷ 4 = 250 ml.
Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.
Method. Change the ribbon to centimetres. Add up what was used. Then take it away from the whole ribbon.
- Change 2 m to centimetres. The pieces are in cm, so we use cm for everything.2 m = 2 × 100 = 200 cm
- Add the two pieces used. Find out how much ribbon was used in total.75 + 60 = 135 cm
- Subtract the total used from the whole ribbon. What is left is the whole ribbon take away what was used.200 − 135 = 65 cm
- Write the answer. 65 cm of ribbon is left.
Check. Add back: 75 + 60 + 65 = 200. ✓
Watch out. Take away the TOTAL used (135 cm), not just one piece.
Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.
Method. First find the mass of the 3 books. Then add the mass of the box. Finally change to kilograms and grams.
- Find the mass of 3 books. Each book is 450 g. Multiply by 3.3 × 450 = 3 × 400 + 3 × 50 = 1,200 + 150 = 1,350 g
- Add the mass of the box. The total mass is the books plus the box.1,350 + 850 = 2,200 g
- Change to kilograms and grams. 1,000 g = 1 kg.2,200 ÷ 1,000 = 2 remainder 200, so 2,200 g = 2 kg 200 g
Check. 2 kg 200 g = 2,200 g. And 850 + 1,350 = 2,200. ✓
Watch out. Work out the 3 books first, then add the box.
Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.
Method. Round each number to the nearest 100 to make an estimate. Then work out the exact answer.
- Round each mass. 598 is close to 600 and 407 is close to 400.598 g ≈ 600 g and 407 g ≈ 400 g
- Add the rounded numbers. These are easy to add. This is our estimate.600 + 400 = 1,000 g
- Work out the exact answer. Use the column method.598 + 407 = 1,005 g
Th H T O 5 9 8 + 4 0 7 1 0 0 5 1 1 1 - Compare. The exact answer should be close to the estimate.1,005 is close to 1,000. The answer is sensible.
Check. 1,005 − 407 = 598. ✓
Watch out. An estimate does not give the exact answer. It tells you if your answer is sensible.
Watch out
Same units first! 1 m + 45 cm is not 46 cm and not 1.45 cm. Change to cm: 100 cm + 45 cm = 145 cm. Also, when you subtract from 1 litre or 1 kilogram, change it to 1,000 ml or 1,000 g first, then use the column method.Exercise 7F Adding, subtracting, multiplying and dividing measures
Non-calculatorKey words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.
Method. Change the measures to the same unit. Then add or subtract the numbers, and give the answer in the unit asked.
- Check the units. We can only add or subtract measures that are in the same unit.Both measures are in centimetres, so we can go straight to the calculation.
- Add the two measures. Add column by column, starting with the ones. Carry when a column makes 10 or more.234 cm + 145 cm = 379 cm
H T O 2 3 4 + 1 4 5 3 7 9 - Write the answer with its unit. A measure always needs its unit.379 cm
Check. Use the inverse: 379 − 145 = 234. ✓
Watch out. You can only add or subtract measures in the same unit. 1 m + 45 cm is not 46 of anything: change it to 145 cm first.
Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.
Method. Change the measures to the same unit. Then add or subtract the numbers, and give the answer in the unit asked.
- Check the units. We can only add or subtract measures that are in the same unit.Both measures are in grams, so we can go straight to the calculation.
- Add the two measures. Add column by column, starting with the ones. Carry when a column makes 10 or more.456 g + 278 g = 734 g
H T O 4 5 6 + 2 7 8 7 3 4 1 1 - Write the answer with its unit. A measure always needs its unit.734 g
Check. Use the inverse: 734 − 278 = 456. ✓
Watch out. You can only add or subtract measures in the same unit. 1 m + 45 cm is not 46 of anything: change it to 145 cm first.
Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.
Method. Change the measures to the same unit. Then add or subtract the numbers, and give the answer in the unit asked.
- Check the units. We can only add or subtract measures that are in the same unit.Both measures are in millilitres, so we can go straight to the calculation.
- Add the two measures. Add column by column, starting with the ones. Carry when a column makes 10 or more.390 ml + 465 ml = 855 ml
H T O 3 9 0 + 4 6 5 8 5 5 1 - Write the answer with its unit. A measure always needs its unit.855 ml
Check. Use the inverse: 855 − 465 = 390. ✓
Watch out. You can only add or subtract measures in the same unit. 1 m + 45 cm is not 46 of anything: change it to 145 cm first.
Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.
Method. Change the measures to the same unit. Then add or subtract the numbers, and give the answer in the unit asked.
- Check the units. We can only add or subtract measures that are in the same unit.Both measures are in metres, so we can go straight to the calculation.
- Add the two measures. Add column by column, starting with the ones. Carry when a column makes 10 or more.2,350 m + 1,475 m = 3,825 m
Th H T O 2 3 5 0 + 1 4 7 5 3 8 2 5 1 - Write the answer with its unit. A measure always needs its unit.3,825 m
Check. Use the inverse: 3,825 − 1,475 = 2,350. ✓
Watch out. You can only add or subtract measures in the same unit. 1 m + 45 cm is not 46 of anything: change it to 145 cm first.
Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.
Method. Change the measures to the same unit. Then add or subtract the numbers, and give the answer in the unit asked.
- Check the units. We can only add or subtract measures that are in the same unit.Both measures are in centimetres, so we can go straight to the calculation.
- Take the smaller measure away from the bigger. Subtract column by column. Exchange when a top digit is too small.785 cm − 340 cm = 445 cm
H T O 7 8 5 − 3 4 0 4 4 5 - Write the answer with its unit. A measure always needs its unit.445 cm
Check. Use the inverse: 445 + 340 = 785. ✓
Watch out. You can only add or subtract measures in the same unit. 1 m + 45 cm is not 46 of anything: change it to 145 cm first.
Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.
Method. Change the measures to the same unit. Then add or subtract the numbers, and give the answer in the unit asked.
- Check the units. We can only add or subtract measures that are in the same unit.Both measures are in grams, so we can go straight to the calculation.
- Take the smaller measure away from the bigger. Subtract column by column. Exchange when a top digit is too small.1,000 g − 650 g = 350 g
Th H T O 0 19 010 00 − 6 5 0 3 5 0 - Write the answer with its unit. A measure always needs its unit.350 g
Check. Use the inverse: 350 + 650 = 1,000. ✓
Watch out. You can only add or subtract measures in the same unit. 1 m + 45 cm is not 46 of anything: change it to 145 cm first.
Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.
Method. Change the measures to the same unit. Then add or subtract the numbers, and give the answer in the unit asked.
- Check the units. We can only add or subtract measures that are in the same unit.Both measures are in millilitres, so we can go straight to the calculation.
- Take the smaller measure away from the bigger. Subtract column by column. Exchange when a top digit is too small.900 ml − 275 ml = 625 ml
H T O 8 99 010 0− 2 7 5 6 2 5 - Write the answer with its unit. A measure always needs its unit.625 ml
Check. Use the inverse: 625 + 275 = 900. ✓
Watch out. You can only add or subtract measures in the same unit. 1 m + 45 cm is not 46 of anything: change it to 145 cm first.
Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.
Method. Change the measures to the same unit. Then add or subtract the numbers, and give the answer in the unit asked.
- Check the units. We can only add or subtract measures that are in the same unit.Both measures are in metres, so we can go straight to the calculation.
- Take the smaller measure away from the bigger. Subtract column by column. Exchange when a top digit is too small.5,000 m − 2,350 m = 2,650 m
Th H T O 4 59 010 00 − 2 3 5 0 2 6 5 0 - Write the answer with its unit. A measure always needs its unit.2,650 m
Check. Use the inverse: 2,650 + 2,350 = 5,000. ✓
Watch out. You can only add or subtract measures in the same unit. 1 m + 45 cm is not 46 of anything: change it to 145 cm first.
Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.
Method. Change the measures to the same unit. Then add or subtract the numbers, and give the answer in the unit asked.
- Change both measures to centimetres. We can only add or subtract measures that are in the same unit. Use the smaller unit so we have whole numbers.2 m 60 cm = 2 × 100 + 60 = 200 + 60 = 260 cm
1 m 55 cm = 1 × 100 + 55 = 100 + 55 = 155 cm - Add the two measures. Add column by column, starting with the ones. Carry when a column makes 10 or more.260 cm + 155 cm = 415 cm
H T O 2 6 0 + 1 5 5 4 1 5 1 - Write the answer in metres and centimetres. 100 cm = 1 m, so divide by 100 and keep the remainder.415 ÷ 100 = 4 remainder 15
415 cm = 4 m 15 cm
Check. Use the inverse: 415 − 155 = 260. ✓
Watch out. You can only add or subtract measures in the same unit. 1 m + 45 cm is not 46 of anything: change it to 145 cm first.
Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.
Method. Change the measures to the same unit. Then add or subtract the numbers, and give the answer in the unit asked.
- Change both measures to grams. We can only add or subtract measures that are in the same unit. Use the smaller unit so we have whole numbers.1 kg 350 g = 1 × 1,000 + 350 = 1,000 + 350 = 1,350 g
2 kg 800 g = 2 × 1,000 + 800 = 2,000 + 800 = 2,800 g - Add the two measures. Add column by column, starting with the ones. Carry when a column makes 10 or more.1,350 g + 2,800 g = 4,150 g
Th H T O 1 3 5 0 + 2 8 0 0 4 1 5 0 1 - Write the answer in kilograms and grams. 1,000 g = 1 kg, so divide by 1,000 and keep the remainder.4,150 ÷ 1,000 = 4 remainder 150
4,150 g = 4 kg 150 g
Check. Use the inverse: 4,150 − 2,800 = 1,350. ✓
Watch out. You can only add or subtract measures in the same unit. 1 m + 45 cm is not 46 of anything: change it to 145 cm first.
Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.
Method. Change the measures to the same unit. Then add or subtract the numbers, and give the answer in the unit asked.
- Change both measures to millilitres. We can only add or subtract measures that are in the same unit. Use the smaller unit so we have whole numbers.3 l 450 ml = 3 × 1,000 + 450 = 3,000 + 450 = 3,450 ml
1 l 650 ml = 1 × 1,000 + 650 = 1,000 + 650 = 1,650 ml - Add the two measures. Add column by column, starting with the ones. Carry when a column makes 10 or more.3,450 ml + 1,650 ml = 5,100 ml
Th H T O 3 4 5 0 + 1 6 5 0 5 1 0 0 1 1 - Write the answer in litres and millilitres. 1,000 ml = 1 l, so divide by 1,000 and keep the remainder.5,100 ÷ 1,000 = 5 remainder 100
5,100 ml = 5 l 100 ml
Check. Use the inverse: 5,100 − 1,650 = 3,450. ✓
Watch out. You can only add or subtract measures in the same unit. 1 m + 45 cm is not 46 of anything: change it to 145 cm first.
Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.
Method. Change the measures to the same unit. Then add or subtract the numbers, and give the answer in the unit asked.
- Change both measures to centimetres. We can only add or subtract measures that are in the same unit. Use the smaller unit so we have whole numbers.3 m 20 cm = 3 × 100 + 20 = 300 + 20 = 320 cm
1 m 85 cm = 1 × 100 + 85 = 100 + 85 = 185 cm - Take the smaller measure away from the bigger. Subtract column by column. Exchange when a top digit is too small.320 cm − 185 cm = 135 cm
H T O 2 311 210 0− 1 8 5 1 3 5 - Write the answer in metres and centimetres. 100 cm = 1 m, so divide by 100 and keep the remainder.135 ÷ 100 = 1 remainder 35
135 cm = 1 m 35 cm
Check. Use the inverse: 135 + 185 = 320. ✓
Watch out. You can only add or subtract measures in the same unit. 1 m + 45 cm is not 46 of anything: change it to 145 cm first.
Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.
Method. Change the measures to the same unit. Then add or subtract the numbers, and give the answer in the unit asked.
- Change both measures to grams. We can only add or subtract measures that are in the same unit. Use the smaller unit so we have whole numbers.5 kg 100 g = 5 × 1,000 + 100 = 5,000 + 100 = 5,100 g
2 kg 450 g = 2 × 1,000 + 450 = 2,000 + 450 = 2,450 g - Take the smaller measure away from the bigger. Subtract column by column. Exchange when a top digit is too small.5,100 g − 2,450 g = 2,650 g
Th H T O 4 510 110 00 − 2 4 5 0 2 6 5 0 - Write the answer in kilograms and grams. 1,000 g = 1 kg, so divide by 1,000 and keep the remainder.2,650 ÷ 1,000 = 2 remainder 650
2,650 g = 2 kg 650 g
Check. Use the inverse: 2,650 + 2,450 = 5,100. ✓
Watch out. You can only add or subtract measures in the same unit. 1 m + 45 cm is not 46 of anything: change it to 145 cm first.
Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.
Method. Change the measures to the same unit. Then add or subtract the numbers, and give the answer in the unit asked.
- Change both measures to millilitres. We can only add or subtract measures that are in the same unit. Use the smaller unit so we have whole numbers.4 l = 4 × 1,000 = 4,000 ml
1 l 250 ml = 1 × 1,000 + 250 = 1,000 + 250 = 1,250 ml - Take the smaller measure away from the bigger. Subtract column by column. Exchange when a top digit is too small.4,000 ml − 1,250 ml = 2,750 ml
Th H T O 3 49 010 00 − 1 2 5 0 2 7 5 0 - Write the answer in litres and millilitres. 1,000 ml = 1 l, so divide by 1,000 and keep the remainder.2,750 ÷ 1,000 = 2 remainder 750
2,750 ml = 2 l 750 ml
Check. Use the inverse: 2,750 + 1,250 = 4,000. ✓
Watch out. You can only add or subtract measures in the same unit. 1 m + 45 cm is not 46 of anything: change it to 145 cm first.
Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.
Method. Change the measures to the same unit. Then add or subtract the numbers, and give the answer in the unit asked.
- Change both measures to grams. We can only add or subtract measures that are in the same unit. Use the smaller unit so we have whole numbers.1.5 kg = 1.5 × 1,000 = 1,500 g
2.25 kg = 2.25 × 1,000 = 2,250 g - Add the two measures. Add column by column, starting with the ones. Carry when a column makes 10 or more.1,500 g + 2,250 g = 3,750 g
Th H T O 1 5 0 0 + 2 2 5 0 3 7 5 0 - Write the answer in kilograms. 1,000 g = 1 kg, so divide by 1,000.3,750 g = 3,750 ÷ 1,000 = 3.75 kg
Check. Use the inverse: 3,750 − 2,250 = 1,500. ✓
Watch out. You can only add or subtract measures in the same unit. 1 m + 45 cm is not 46 of anything: change it to 145 cm first.
Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.
Method. Change the measures to the same unit. Then add or subtract the numbers, and give the answer in the unit asked.
- Change both measures to centimetres. We can only add or subtract measures that are in the same unit. Use the smaller unit so we have whole numbers.3.4 m = 3.4 × 100 = 340 cm
1.85 m = 1.85 × 100 = 185 cm - Add the two measures. Add column by column, starting with the ones. Carry when a column makes 10 or more.340 cm + 185 cm = 525 cm
H T O 3 4 0 + 1 8 5 5 2 5 1 - Write the answer in metres. 100 cm = 1 m, so divide by 100.525 cm = 525 ÷ 100 = 5.25 m
Check. Use the inverse: 525 − 185 = 340. ✓
Watch out. You can only add or subtract measures in the same unit. 1 m + 45 cm is not 46 of anything: change it to 145 cm first.
Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.
Method. Change the measures to the same unit. Then add or subtract the numbers, and give the answer in the unit asked.
- Change both measures to millilitres. We can only add or subtract measures that are in the same unit. Use the smaller unit so we have whole numbers.5 l = 5 × 1,000 = 5,000 ml
2.5 l = 2.5 × 1,000 = 2,500 ml - Take the smaller measure away from the bigger. Subtract column by column. Exchange when a top digit is too small.5,000 ml − 2,500 ml = 2,500 ml
Th H T O 4 510 00 0 − 2 5 0 0 2 5 0 0 - Write the answer in litres. 1,000 ml = 1 l, so divide by 1,000.2,500 ml = 2,500 ÷ 1,000 = 2.5 l
Check. Use the inverse: 2,500 + 2,500 = 5,000. ✓
Watch out. You can only add or subtract measures in the same unit. 1 m + 45 cm is not 46 of anything: change it to 145 cm first.
Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.
Method. Multiply the measure by 3. Keep the unit.
- Multiply each part of 250 by 3. Splitting the number into hundreds, tens and ones makes the times tables easier (the distributive law).3 × 200 = 600
3 × 50 = 150
600 + 150 = 750 - Write the total with its unit. 750 g
Check. Divide back: 750 ÷ 3 = 250. ✓
Watch out. The unit stays the same when you multiply by a number. 4 lots of 350 ml is still in ml.
Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.
Method. Multiply the measure by 5. Keep the unit.
- Multiply each part of 120 by 5. Splitting the number into hundreds, tens and ones makes the times tables easier (the distributive law).5 × 100 = 500
5 × 20 = 100
500 + 100 = 600 - Write the total with its unit. 600 ml
Check. Divide back: 600 ÷ 5 = 120. ✓
Watch out. The unit stays the same when you multiply by a number. 4 lots of 350 ml is still in ml.
Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.
Method. Multiply the measure by 4. Keep the unit.
- Multiply each part of 275 by 4. Splitting the number into hundreds, tens and ones makes the times tables easier (the distributive law).4 × 200 = 800
4 × 70 = 280
4 × 5 = 20
800 + 280 + 20 = 1,100 - Write the total with its unit. 1,100 cm
Check. Divide back: 1,100 ÷ 4 = 275. ✓
Watch out. The unit stays the same when you multiply by a number. 4 lots of 350 ml is still in ml.
Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.
Method. Multiply the measure by 6. Keep the unit.
- Multiply each part of 150 by 6. Splitting the number into hundreds, tens and ones makes the times tables easier (the distributive law).6 × 100 = 600
6 × 50 = 300
600 + 300 = 900 - Write the total with its unit. 900 g
Check. Divide back: 900 ÷ 6 = 150. ✓
Watch out. The unit stays the same when you multiply by a number. 4 lots of 350 ml is still in ml.
Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.
Method. Share by dividing. Work in the small unit and keep the unit.
- Divide 600 by 3. Use a times-table fact. 6 ÷ 3 = 2, and 600 is 6 × 100.6 ÷ 3 = 2
2 × 100 = 200 g - Write the answer with its unit. A measure always needs its unit.200 g
Check. Multiply back: 3 × 200 = 600. ✓
Watch out. Change to the small unit first, so you have a whole number to divide. 1 l shared between 4 is 1,000 ml ÷ 4 = 250 ml.
Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.
Method. Share by dividing. Work in the small unit and keep the unit.
- Divide 1,500 by 5. Use a times-table fact. 15 ÷ 5 = 3, and 1,500 is 15 × 100.15 ÷ 5 = 3
3 × 100 = 300 ml - Write the answer with its unit. A measure always needs its unit.300 ml
Check. Multiply back: 5 × 300 = 1,500. ✓
Watch out. Change to the small unit first, so you have a whole number to divide. 1 l shared between 4 is 1,000 ml ÷ 4 = 250 ml.
Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.
Method. Share by dividing. Work in the small unit and keep the unit.
- Divide 2,000 by 4. Use a times-table fact. 20 ÷ 4 = 5, and 2,000 is 20 × 100.20 ÷ 4 = 5
5 × 100 = 500 cm - Write the answer with its unit. A measure always needs its unit.500 cm
Check. Multiply back: 4 × 500 = 2,000. ✓
Watch out. Change to the small unit first, so you have a whole number to divide. 1 l shared between 4 is 1,000 ml ÷ 4 = 250 ml.
Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.
Method. Share by dividing. Work in the small unit and keep the unit.
- Divide 2,400 by 6. Use a times-table fact. 24 ÷ 6 = 4, and 2,400 is 24 × 100.24 ÷ 6 = 4
4 × 100 = 400 g - Write the answer with its unit. A measure always needs its unit.400 g
Check. Multiply back: 6 × 400 = 2,400. ✓
Watch out. Change to the small unit first, so you have a whole number to divide. 1 l shared between 4 is 1,000 ml ÷ 4 = 250 ml.
Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.
Method. Change the measures to the same unit. Then add or subtract the numbers, and give the answer in the unit asked.
- Change both measures to grams. We can only add or subtract measures that are in the same unit. Use the smaller unit so we have whole numbers.1 kg = 1 × 1,000 = 1,000 g
- Take the smaller measure away from the bigger. Subtract column by column. Exchange when a top digit is too small.1,000 g − 450 g = 550 g
Th H T O 0 19 010 00 − 4 5 0 5 5 0 - Write the answer with its unit. A measure always needs its unit.550 g
Check. Use the inverse: 550 + 450 = 1,000. ✓
Watch out. You can only add or subtract measures in the same unit. 1 m + 45 cm is not 46 of anything: change it to 145 cm first.
Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.
Method. Change the measures to the same unit. Then add or subtract the numbers, and give the answer in the unit asked.
- Change both measures to millilitres. We can only add or subtract measures that are in the same unit. Use the smaller unit so we have whole numbers.1 l = 1 × 1,000 = 1,000 ml
- Take the smaller measure away from the bigger. Subtract column by column. Exchange when a top digit is too small.1,000 ml − 275 ml = 725 ml
Th H T O 0 19 09 010 0− 2 7 5 7 2 5 - Write the answer with its unit. A measure always needs its unit.725 ml
Check. Use the inverse: 725 + 275 = 1,000. ✓
Watch out. You can only add or subtract measures in the same unit. 1 m + 45 cm is not 46 of anything: change it to 145 cm first.
Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.
Method. Change the measures to the same unit. Then add or subtract the numbers, and give the answer in the unit asked.
- Change both measures to centimetres. We can only add or subtract measures that are in the same unit. Use the smaller unit so we have whole numbers.1 m = 1 × 100 = 100 cm
- Take the smaller measure away from the bigger. Subtract column by column. Exchange when a top digit is too small.100 cm − 35 cm = 65 cm
H T O 0 19 010 0− 3 5 6 5 - Write the answer with its unit. A measure always needs its unit.65 cm
Check. Use the inverse: 65 + 35 = 100. ✓
Watch out. You can only add or subtract measures in the same unit. 1 m + 45 cm is not 46 of anything: change it to 145 cm first.
Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.
Method. Change the measures to the same unit. Then add or subtract the numbers, and give the answer in the unit asked.
- Change both measures to grams. We can only add or subtract measures that are in the same unit. Use the smaller unit so we have whole numbers.2 kg = 2 × 1,000 = 2,000 g
- Take the smaller measure away from the bigger. Subtract column by column. Exchange when a top digit is too small.2,000 g − 750 g = 1,250 g
Th H T O 1 29 010 00 − 7 5 0 1 2 5 0 - Write the answer with its unit. A measure always needs its unit.1,250 g
Check. Use the inverse: 1,250 + 750 = 2,000. ✓
Watch out. You can only add or subtract measures in the same unit. 1 m + 45 cm is not 46 of anything: change it to 145 cm first.
Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.
Method. Change the measures to the same unit. Then add or subtract the numbers, and give the answer in the unit asked.
- Change both measures to metres. We can only add or subtract measures that are in the same unit. Use the smaller unit so we have whole numbers.1.5 km = 1.5 × 1,000 = 1,500 m
2.25 km = 2.25 × 1,000 = 2,250 m - Add the two measures. Add column by column, starting with the ones. Carry when a column makes 10 or more.1,500 m + 2,250 m = 3,750 m
Th H T O 1 5 0 0 + 2 2 5 0 3 7 5 0 - Write the answer in kilometres. 1,000 m = 1 km, so divide by 1,000.3,750 m = 3,750 ÷ 1,000 = 3.75 km
Check. Use the inverse: 3,750 − 2,250 = 1,500. ✓
Watch out. You can only add or subtract measures in the same unit. 1 m + 45 cm is not 46 of anything: change it to 145 cm first.
Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.
Method. Share by dividing. Work in the small unit and keep the unit.
- Change the measure to millilitres. Work in the smaller unit so we have a whole number.1 l = 1 × 1,000 = 1,000 ml
- Divide 1,000 by 4. Use a times-table fact. 100 ÷ 4 = 25, and 1,000 is 100 × 10.100 ÷ 4 = 25
25 × 10 = 250 ml - Write the answer with its unit. A measure always needs its unit.250 ml
Check. Multiply back: 4 × 250 = 1,000. ✓
Watch out. Change to the small unit first, so you have a whole number to divide. 1 l shared between 4 is 1,000 ml ÷ 4 = 250 ml.
Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.
Method. Do not add 1 and 45. Change 1 m to centimetres first.
- Look at what Leo did. Leo added the numbers 1 and 45 and wrote cm.1 + 45 = 46, so Leo wrote 46 cm.
- Find the mistake. 1 m and 45 cm are in different units. 1 m is much bigger than 1 cm.1 m = 100 cm
- Work out the correct answer. Now both are in cm.100 + 45 = 145 cm = 1 m 45 cm
Check. 145 cm is more than 1 m, but 46 cm is less than 1 m. ✓
Watch out. Change to the same unit before you add.
Exercise 7G Measure problems
Non-calculatorKey words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.
Method. Change 3 m to centimetres. Then take away the piece that was cut off.
- Change 3 m to centimetres. The piece is 1 m 25 cm, so we can use cm for everything.3 m = 300 cm and 1 m 25 cm = 125 cm
- Subtract the piece from the ribbon. What is left is the whole ribbon take away the piece.300 − 125 = 175 cm
- Write the answer in metres and centimetres. 100 cm = 1 m.175 cm = 1 m 75 cm
Check. 125 + 175 = 300. ✓
Watch out. Change both lengths to cm first.
Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.
Method. Multiply the measure by 3. Keep the unit.
- Change the measure to grams. Work in the smaller unit so we have a whole number.1.5 kg = 1.5 × 1,000 = 1,500 g
- Multiply each part of 1,500 by 3. Splitting the number into hundreds, tens and ones makes the times tables easier (the distributive law).3 × 1,000 = 3,000
3 × 500 = 1,500
3,000 + 1,500 = 4,500 - Write the total with its unit. 4,500 g
- Write the answer in kilograms. 1,000 g = 1 kg.4,500 ÷ 1,000 = 4.5 kg
Check. Divide back: 4,500 ÷ 3 = 1,500. ✓
Watch out. The unit stays the same when you multiply by a number. 4 lots of 350 ml is still in ml.
Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.
Method. Multiply the measure by 4. Keep the unit.
- Multiply each part of 750 by 4. Splitting the number into hundreds, tens and ones makes the times tables easier (the distributive law).4 × 700 = 2,800
4 × 50 = 200
2,800 + 200 = 3,000 - Write the total with its unit. 3,000 ml
Check. Divide back: 3,000 ÷ 4 = 750. ✓
Watch out. The unit stays the same when you multiply by a number. 4 lots of 350 ml is still in ml.
Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.
Method. Multiply the measure by 4. Keep the unit.
- Multiply each part of 750 by 4. Splitting the number into hundreds, tens and ones makes the times tables easier (the distributive law).4 × 700 = 2,800
4 × 50 = 200
2,800 + 200 = 3,000 - Write the total with its unit. 3,000 ml
- Write the answer in litres. 1,000 ml = 1 l.3,000 ÷ 1,000 = 3 l
Check. Divide back: 3,000 ÷ 4 = 750. ✓
Watch out. The unit stays the same when you multiply by a number. 4 lots of 350 ml is still in ml.
Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.
Method. Find the mass of the 3 books, then add the box. Then write the answer in kg and g.
- Find the mass of 3 books. Each book is 450 g.3 × 450 = 1,350 g
- Add the box. The box is 850 g.1,350 + 850 = 2,200 g
- Change to kilograms and grams. 1,000 g = 1 kg.2,200 g = 2 kg 200 g
Check. 2 kg 200 g = 2,200 g. ✓
Watch out. Multiply first, then add.
Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.
Method. Change the measures to the same unit. Then add or subtract the numbers, and give the answer in the unit asked.
- Change both measures to metres. We can only add or subtract measures that are in the same unit. Use the smaller unit so we have whole numbers.1.4 km = 1.4 × 1,000 = 1,400 m
- Add the two measures. Add column by column, starting with the ones. Carry when a column makes 10 or more.1,400 m + 800 m = 2,200 m
Th H T O 1 4 0 0 + 8 0 0 2 2 0 0 1 - Write the answer with its unit. A measure always needs its unit.2,200 m
Check. Use the inverse: 2,200 − 800 = 1,400. ✓
Watch out. You can only add or subtract measures in the same unit. 1 m + 45 cm is not 46 of anything: change it to 145 cm first.
Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.
Method. Change the measures to the same unit. Then add or subtract the numbers, and give the answer in the unit asked.
- Change both measures to metres. We can only add or subtract measures that are in the same unit. Use the smaller unit so we have whole numbers.1.4 km = 1.4 × 1,000 = 1,400 m
- Add the two measures. Add column by column, starting with the ones. Carry when a column makes 10 or more.1,400 m + 800 m = 2,200 m
Th H T O 1 4 0 0 + 8 0 0 2 2 0 0 1 - Write the answer in kilometres. 1,000 m = 1 km, so divide by 1,000.2,200 m = 2,200 ÷ 1,000 = 2.2 km
Check. Use the inverse: 2,200 − 800 = 1,400. ✓
Watch out. You can only add or subtract measures in the same unit. 1 m + 45 cm is not 46 of anything: change it to 145 cm first.
Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.
Method. Change 5 litres to millilitres. Then find how many 250 ml cups fit.
- Change 5 l to millilitres. 1 l = 1,000 ml.5 × 1,000 = 5,000 ml
- Divide by the size of one cup. The number of cups is how many lots of 250 ml are in 5,000 ml. 4 cups make 1,000 ml, so 5 litres is 5 × 4 cups.1,000 ÷ 250 = 4 cups in 1 litre, so 5 × 4 = 20
- Write the answer. 20 cups fill the bucket.
Check. 20 × 250 = 5,000. ✓
Watch out. Change to millilitres before you divide.
Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.
Method. Change the measures to the same unit. Then add or subtract the numbers, and give the answer in the unit asked.
- Change both measures to centimetres. We can only add or subtract measures that are in the same unit. Use the smaller unit so we have whole numbers.3.5 m = 3.5 × 100 = 350 cm
2 m 80 cm = 2 × 100 + 80 = 200 + 80 = 280 cm - Take the smaller measure away from the bigger. Subtract column by column. Exchange when a top digit is too small.350 cm − 280 cm = 70 cm
H T O 2 315 50 − 2 8 0 7 0 - Write the answer with its unit. A measure always needs its unit.70 cm
Check. Use the inverse: 70 + 280 = 350. ✓
Watch out. You can only add or subtract measures in the same unit. 1 m + 45 cm is not 46 of anything: change it to 145 cm first.
Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.
Method. Round each mass to the nearest 100 g and add.
- Round each mass. 295 is close to 300 and 410 is close to 400.295 g ≈ 300 g 410 g ≈ 400 g
- Add the rounded masses. 300 + 400 = 700 g
Check. The exact total is 705 g, which is close to 700 g. ✓
Watch out. Round each number first.
Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.
Method. Change the measures to the same unit. Then add or subtract the numbers, and give the answer in the unit asked.
- Check the units. We can only add or subtract measures that are in the same unit.Both measures are in grams, so we can go straight to the calculation.
- Add the two measures. Add column by column, starting with the ones. Carry when a column makes 10 or more.295 g + 410 g = 705 g
H T O 2 9 5 + 4 1 0 7 0 5 1 - Write the answer with its unit. A measure always needs its unit.705 g
Check. Use the inverse: 705 − 410 = 295. ✓
Watch out. You can only add or subtract measures in the same unit. 1 m + 45 cm is not 46 of anything: change it to 145 cm first.
Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.
Method. Multiply the measure by 3. Keep the unit.
- Multiply by 3. Use a times-table fact and the place value.3 × 300 = 900
- Write the total with its unit. 900 g
Check. Divide back: 900 ÷ 3 = 300. ✓
Watch out. The unit stays the same when you multiply by a number. 4 lots of 350 ml is still in ml.
Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.
Method. Find the mass of 3 bags, then compare with 1 kg (1,000 g).
- Multiply to find the mass of 3 bags. Each bag is 350 g.3 × 350 = 3 × 300 + 3 × 50 = 900 + 150 = 1,050 g
- Change 1 kg to grams. We compare in the same unit.1 kg = 1,000 g
- Compare. 1,050 g is more than 1,000 g, so Zoe is right. The 3 bags are 50 g more than 1 kg.
Check. 1,050 − 1,000 = 50. ✓
Watch out. Compare in the same unit.
Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.
Method. Change 2 m to centimetres and subtract 75 cm. Then change the answer to metres and centimetres.
- Change 2 m to centimetres. 1 m = 100 cm.2 m = 200 cm
- Subtract 75 cm. Both are in cm now.200 − 75 = 125 cm
- Change to metres and centimetres. 125 cm is 100 cm and 25 cm.125 cm = 1 m 25 cm
- Compare with Sam’s answer. Sam said 1 m 25 cm. He is right.
Check. 1 m 25 cm + 75 cm = 200 cm = 2 m. ✓
Watch out. Check by adding back.
Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.
Method. Change every mass to grams. Add them up. Then compare with 5 kg = 5,000 g.
- Change the masses to grams. 1.2 kg = 1,200 g and 2.5 kg = 2,500 g. 850 g is already in grams.1.2 kg = 1,200 g 850 g 2.5 kg = 2,500 g
- Add the three masses. 1,200 + 850 = 2,050 and 2,050 + 2,500 = 4,550 g
- Change the limit to grams. 5 kg = 5 × 1,000.5 kg = 5,000 g
- Compare and find the space left. 4,550 is less than 5,000.5,000 − 4,550 = 450 g. Yes, they can all go together, with 450 g to spare.
Check. 4,550 + 450 = 5,000. ✓
Watch out. Change every measure to grams first.