NumihanaFor 503 − 278, three ones are not enough to subtract eight ones. The tens column has zero, so there is no ten there to exchange yet. Begin at hundreds: exchange one hundred for ten tens, then exchange one of those tens for ten ones.
Work through the example
- Align 503 and 278. Estimate 500 − 280 = 220.
- Exchange one hundred: 4 hundreds, 10 tens and 3 ones remain.
- Exchange one of those tens: 4 hundreds, 9 tens and 13 ones remain. Nine tens stay because one of the ten tens was exchanged.
- Subtract 13 − 8 = 5 ones, 9 − 7 = 2 tens and 4 − 2 = 2 hundreds. The answer is 225. Check 225 + 278 = 503.
Why it works
There are two linked exchanges. After each one, the amount remains 503. The working row shows the final available units; crossed original digits indicate which original amounts have changed. Work one place at a time rather than trying to change every digit at once.
A common slip
Keeping ten tens while also creating ten extra ones counts one ten twice. Ask “How many tens remain after one is exchanged?” The answer is nine, not ten.
For teachers & parents
Use the ordinary one-ten exchange guide first. Let the learner draw the intermediate ten tens before crossing to nine. A worksheet can require exchanges through zero for focused practice, but alternate written or mental strategies remain valid; the final-answer checker does not grade the working row.
Talk it through
Try explaining 806 − 479. After exchanging through zero, why are there 7 hundreds, 9 tens and 16 ones?
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