NumihanaIn 542 − 218, there are two ones in the top row and eight ones to subtract. We cannot complete that ones subtraction using just the two ones. Exchange one of the four tens for ten ones. The top amount is still 542, expressed in different units.
Work through the example
- Align 542 and 218. An estimate using 540 − 220 gives about 320.
- Exchange one ten for ten ones: 5 hundreds, 3 tens and 12 ones remain. Mark the changed top digits in the working row.
- Subtract ones: 12 − 8 = 4. Subtract tens: 3 − 1 = 2. Subtract hundreds: 5 − 2 = 3.
- The answer is 324. Check by adding 324 + 218 = 542.
Why it works
Exchanging changes the way we represent the amount, not the amount itself: 500 + 40 + 2 equals 500 + 30 + 12. The updated tens digit matters when we reach that column.
A common slip
Subtracting 2 from 8 instead would reverse the calculation in one column. Leaving four tens after creating twelve ones would add ten to the top amount. Record both sides of the exchange together.
For teachers & parents
Before introducing an exchange, confirm that the learner can subtract a question with enough units in every column. Use base-ten drawings to show one ten becoming ten ones. Ask the learner to read the changed top amount to establish that its value stays constant.
Talk it through
Explain why 5 hundreds, 3 tens and 12 ones is still 542. Which column changes first when you exchange?
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