More addition & subtraction
Subtraction: regrouping tens
Sometimes there are not enough tens in the tens place to subtract from. Then you regroup 1 hundred as 10 tens. You also estimate first and use trial and improvement to find unknown numbers.
Regrouping a hundred as tens
When the tens you have are not enough to subtract from, exchange 1 hundred for 10 tens. Example: 246 − 84. The tens are 4 tens − 8 tens, which is not enough. Regroup: 246 = 100 + 140 + 6. Now 14 tens − 8 tens = 6 tens.
Writing a regrouped number
To regroup, exchange 1 hundred for 10 tens. 235 = 100 + 130 + 5 (1 hundred, 13 tens, 5 ones). 452 = 300 + 150 + 2 (3 hundreds, 15 tens, 2 ones).
Estimate first
Round each number to the nearest 10 and subtract those to estimate. Example: for 534 − 93, round to 530 − 90 = 440. Your real answer should be close to 440.
Trial and improvement
To find an unknown number, pick a sensible starting point, check it, then make a small change to get closer. Example: 147 − ? = 63. Start: 147 − 47 = 100, so the answer is less than 100. 63 is 16 less than 100, so subtract 16 more to get 84.
Checking your answer
Subtraction undoes addition, so you can check a subtraction by adding your answer to the number you took away. Example: check 518 − 248 = 270 by working out 270 + 248 = 518.
Worked examples
Regrouping a hundred as tens
- Work out 246 − 84.
- Ones: 6 − 4 = 2.
- Tens: 4 tens is not enough to take 8 tens, so regroup 1 hundred as 10 tens → 14 tens.
- 14 tens − 8 tens = 6 tens, and 1 hundred is left.
Answer: 246 − 84 = 162
Estimate then subtract
- Work out 534 − 93.
- Estimate: 530 − 90 = 440.
- Subtract, regrouping a hundred for the tens: 13 tens − 9 tens = 4 tens.
- Answer 441 is close to the estimate 440.
Answer: 534 − 93 = 441
Trial and improvement
- Find the unknown: 147 − ? = 63.
- Start: 147 − 47 = 100, so the answer is less than 100.
- 63 is 16 less than 100, so subtract 16 more.
- 100 − 16 = 84.
Answer: The unknown is 84.
Checking with the inverse
- You worked out 518 − 248 = 270.
- Check by adding the answer to the number you took away.
- 270 + 248 = 518, which matches the start.
Answer: The subtraction is correct: 518 − 248 = 270.
Where you see this in real life
- Working out how many T-shirts are left after some are collected.
- Finding how many children are somewhere when you know the total and the adults.
- Sharing marbles equally between two people.
Key words
- Regroup
- To swap 1 hundred for 10 tens (or 1 ten for 10 ones) when a place value does not have enough.
- Exchange
- Another word for regroup — trading between place values.
- Trial and improvement
- Try a number, check it, then make a small change to get closer.
- Unknown
- A missing number you are trying to find, sometimes shown by a symbol.
- Estimate
- A close guess of the answer, often found by rounding to the nearest 10.