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Written Subtraction with Trading

Maths · Y3 Add & Subtract
Year 3
Lesson Guide
Explanation
Written subtraction uses the same tidy columns as addition: line up from the right, and always put the bigger number on top. 76 − 43: ones first, 6 − 3 = 3. Then tens, 7 − 4 = 3. Answer 33. When every top digit is big enough, it's this simple.
Your Turn
Set out and solve 89 − 56. Check: ones 9−6=3, tens 8−5=3 → 33.
Watch Out
The bigger number goes on top — 43 − 76 is a different (and for now impossible!) question.
Explanation
Sometimes the top digit is too small: in 52 − 28, the ones ask 2 − 8 — can't do it! So TRADE: break one of the 5 tens into 10 ones. Now the ones column has 12, and the tens column has only 4 left. 12 − 8 = 4, then 4 − 2 = 2. Answer: 24. Cross out the 5, write 4, and put a little 1 next to the 2 — that's the paperwork of the trade.
Your Turn
Work 63 − 27 with a trade. Check: 13 − 7 = 6, then 5 − 2 = 3 → 36.
Watch Out
NEVER flip the digits! 2 − 8 does not become 8 − 2. If the top is too small, trade — don't swap.
Explanation
With three digits, the trade can happen in any column. 435 − 182: ones are fine, 5 − 2 = 3. But the tens ask 3 − 8 — stuck! Trade one HUNDRED into 10 tens: now it's 13 − 8 = 5, and the hundreds drop from 4 to 3. Finish: 3 − 1 = 2. Answer: 253. Same trick, just one column over.
Your Turn
Work 524 − 261. Check: ones 4−1=3; tens 2−6 stuck → trade: 12−6=6; hundreds 4−2=2 → 263.
Watch Out
After a trade, remember the column you borrowed from is now one smaller — cross it out and write its new value.
Explanation
The trickiest trade: 405 − 178. The ones need to borrow, but the tens column holds 0 — nothing to lend! So the tens borrow from the hundreds first (hundreds 4 → 3, tens 0 → 10), and THEN the ones borrow from the tens (tens 10 → 9, ones 5 → 15). Now subtract: 15 − 8 = 7, 9 − 7 = 2, 3 − 1 = 2. Answer: 227. Two knocks on two doors.
Your Turn
Work 603 − 245. Check: double trade → 13−5=8, 9−4=5, 5−2=3 → 358.
Watch Out
After the double trade the middle column is 9, not 10 — it lent one of its new tens straight on to the ones.
Explanation
Subtraction has a built-in checker: add your answer back to what you took away, and you should land exactly on the starting number. 435 − 182 = 253? Check: 253 + 182 = 435 ✓. If the add-back misses, one of your trades slipped — go hunt for it. Finish every column subtraction with this ten-second check.
Your Turn
You worked 524 − 261 = 263 earlier. Add back to check: 263 + 261 = ? Check: 524 ✓. Now the quiz and exercises!
Watch Out
Check with ADDITION, not by redoing the subtraction — redoing it often repeats the same mistake.
Step 1: Introduction
Step 1 of 5
76 − 43, set out in columns 7 6 − 4 3 3 3 Big number on TOP · line up from the right · ones first. ones: 6 − 3 = 3 · tens: 7 − 4 = 3 → 33
52 − 28 — the ones are stuck 5 4 1 5 2 − 2 8 2 4 2 − 8 can't be done… so trade 1 ten for 10 ones: 12 − 8 = 4. The 5 tens become 4 tens: 4 − 2 = 2 → answer 24.
435 − 182 4 3 5 − 1 8 2 2 5 3 ones: 5 − 2 = 3 ✓ · tens: 3 − 8 stuck! Trade a hundred: 13 − 8 = 5 hundreds: 3 − 1 = 2 → answer 253
405 − 178 — the neighbour is 0! 4 0 5 − 1 7 8 2 2 7 Ones need a ten, but the tens hold 0 — knock on the hundreds' door! Trade a hundred → tens become 10. Trade a ten → tens 9, ones 15. Then: 15 − 8 = 7 · 9 − 7 = 2 · 3 − 1 = 2 → 227
Was 435 − 182 = 253 right? 253 + 182 = ? 435 ✓ Answer + what you took away = what you started with. If adding back doesn't return the start number, a trade went wrong. This check catches almost every mistake. Now do the quiz!
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