The idea, step by step
Make a new ten or hundred
In 267 + 158, the ones give 7 + 8 = 15. Fifteen ones is 1 ten and 5 ones. Keep 5 ones and add the new ten to the tens column.
The tens then give 6 + 5 + 1 = 12 tens. Twelve tens is 1 hundred and 2 tens. Add that new hundred to the hundreds. Every exchange keeps the total amount the same.
Exchange before subtracting
For 352 − 128, 2 ones is not enough to remove 8 ones. Exchange one of the 5 tens for 10 ones. You now have 3 hundreds, 4 tens and 12 ones.
Subtract 8 ones, 2 tens and 1 hundred. The answer has 2 hundreds, 2 tens and 4 ones: 224. You are renaming 352, not adding an extra ten to it.
A common trap
Changing 352 into 3 hundreds, 5 tens and 12 ones before subtracting.
Instead: The ten exchanged into ones must leave the tens column. The correct renaming is 3 hundreds, 4 tens and 12 ones.
See the thinking
Regroup when adding
Calculate 267 + 158.
- 7 + 8 = 15 ones: write 5 ones and regroup 1 ten.
- 6 + 5 + 1 = 12 tens: write 2 tens and regroup 1 hundred.
- 2 + 1 + 1 = 4 hundreds.
Exchange a hundred
Calculate 403 − 176.
- Rename 403 as 3 hundreds, 9 tens and 13 ones.
- 13 − 6 = 7 ones.
- 9 − 7 = 2 tens.
- 3 − 1 = 2 hundreds.
Check your understanding
Calculate 64 − 28.
Show answer
36
Rename 64 as 5 tens and 14 ones. Remove 2 tens and 8 ones.
Your turn
6 questions · Work at your own pace.
Read the questions online
- Calculate 48 + 27.
- Calculate 176 + 245.
- Calculate 82 − 47.
- Calculate 501 − 268.
- A box holds 258 pencils. Another 167 are added. How many are there now?
- A school prints 430 notes and gives out 185. How many are left?
Read the worked solutions
- Calculate 48 + 27.
8 + 7 = 15 ones; 4 + 2 + 1 = 7 tens.
75 - Calculate 176 + 245.
6 + 5 = 11 ones; 7 + 4 + 1 = 12 tens; 1 + 2 + 1 = 4 hundreds.
421 - Calculate 82 − 47.
Rename 82 as 7 tens and 12 ones; 12 − 7 = 5 and 7 − 4 = 3.
35 - Calculate 501 − 268.
Rename 501 as 4 hundreds, 9 tens and 11 ones; subtract by place.
233 - A box holds 258 pencils. Another 167 are added. How many are there now?
258 + 167: 8 + 7 = 15 ones, 5 + 6 + 1 = 12 tens, 2 + 1 + 1 = 4 hundreds.
425 pencils - A school prints 430 notes and gives out 185. How many are left?
430 can be renamed as 3 hundreds, 12 tens and 10 ones; subtract 1 hundred, 8 tens and 5 ones.
245 notes
Curriculum reference & lesson scope
Australian Curriculum v9 / SA Curriculum Mathematics
Mental strategies; two-/three-digit calculations; regrouping; inverse operations; missing values.
Official curriculum source ↗