More addition & subtraction
Complements
A complement is a number you add to another to make a total. As numbers get larger, counting on is slow — it is quicker to use known number bonds and calculate mentally.
Complements of 100
Two numbers are complements of 100 when they add to make 100. Use your number bonds to 10: 35 + 65 = 100, because 5 + 5 = 10 (ones) and 30 + 60 = 90 (tens), giving 100. To find a complement, work out 100 − the number.
Complements of 1000
If you know a complement of 100, make each number ten times larger to get a complement of 1000. 35 + 65 = 100 → 350 + 650 = 1000. 500 + 500 = 1000 is a complement of 1000 too.
Complements of other multiples
You can find the number that makes another multiple of 10 or 100. Example: 340 + ? = 570. Work out 570 − 340 = 230, so 340 + 230 = 570. Always calculate mentally.
Mental estimates with multiples of 10
When numbers are multiples of 10, think in tens. Example: 980 − 260. That is 98 tens − 26 tens = 72 tens = 720. This is much quicker than counting back.
Worked examples
Complement of 100
- Find the complement of 100 for 35.
- Work out 100 − 35.
- Check: 35 + 65 = 100.
Answer: The complement is 65.
Complement of 1000
- You know 35 + 65 = 100.
- Make each number ten times larger.
- 35 → 350 and 65 → 650.
Answer: 350 + 650 = 1000.
Complement of another multiple
- Find the missing number: 340 + ? = 570.
- Calculate mentally: 570 − 340.
- Check: 340 + 230 = 570.
Answer: The missing number is 230.
Mental estimate
- Calculate 980 − 260 mentally.
- Both are multiples of 10, so think in tens.
- 98 tens − 26 tens = 72 tens.
Answer: 980 − 260 = 720.
Where you see this in real life
- Working out how much more money you need to reach 100 pence.
- Finding how far you still have to travel to reach 1000 metres.
- Quickly estimating totals when shopping with round prices.
Key words
- Complement
- A number you add to another to make a given total, such as 100 or 1000.
- Number bond
- A pair of numbers that add to make a total, like 3 + 7 = 10.
- Mentally
- Working out an answer in your head, without writing every step.
- Multiple of 10
- A number in the 10 times table, such as 30, 250 or 1000.
- Estimate
- A close, quick answer, often using round numbers.