Addition & Subtraction • Topic 2 of 5

Subtraction

Subtraction carries three meanings a teacher should keep separate: taking away (5 sweets, eat 2), comparing (how much taller is one child than another), and finding a missing part (how many more to reach a target). All three are the same operation, but children meet them as different situations, and word problems exploit that. Mechanically, multi-digit subtraction aligns by place value and works from the ones, just like addition. The concept that trips children, and that CTET targets, is borrowing, also called regrouping or decomposing. When the top digit is smaller than the one below it, you take one unit from the next column to the left; that borrowed unit is worth ten in the current column, and the column you took from drops by one. In 53 - 28 the ones show 3 below 8, so borrow: the 5 tens become 4, the 3 ones become 13, and 13 - 8 = 5; the tens give 4 - 2 = 2, answer 25. Borrowing across a zero is the hardest case and a favourite trap. In 402 - 135 there are no tens to borrow, so you first regroup the hundreds (4 becomes 3, giving 10 tens), then borrow one of those tens for the ones (10 tens become 9, the 2 ones become 12); now 12 - 5 = 7, 9 - 3 = 6, 3 - 1 = 2, answer 267. The honest check is always the inverse: difference plus subtrahend should rebuild the minuend.

✅ Solved examples

1. Subtract 53 - 28 and explain the borrowing.
Ones: 3 is less than 8, so borrow 1 ten from the 5. The 5 becomes 4 and the 3 becomes 13. Then 13 - 8 = 5. Tens: 4 - 2 = 2. The answer is 25. Check: 25 + 28 = 53.
2. Find 402 - 135 (borrowing across a zero).
Ones need a borrow but the tens digit is 0. Regroup the hundreds first: 4 hundreds become 3, giving 10 tens. Now borrow 1 ten for the ones: 10 tens become 9, and the 2 ones become 12. Ones: 12 - 5 = 7. Tens: 9 - 3 = 6. Hundreds: 3 - 1 = 2. The answer is 267. Check: 267 + 135 = 402.
3. Compute 456 - 132 and say whether any borrowing is needed.
Ones: 6 - 2 = 4. Tens: 5 - 3 = 2. Hundreds: 4 - 1 = 3. The answer is 324. No borrowing is needed because every top digit is already larger than the digit below it.
4. Use the fact family of 15 to find 15 - 7 without counting back.
Since 7 + 8 = 15, the same fact family gives 15 - 7 = 8. Knowing addition facts gives the matching subtraction facts for free.

✏️ Practice — try these, take hints as needed

1. Subtract 71 - 26.
Ones: 1 is less than 6, so borrow.
11 - 6 = 5.
45
2. Find 600 - 247 (borrowing across two zeros).
Regroup the hundreds, then the tens.
Check with 247 + answer.
353
3. Verify whether 824 - 391 = 433 is correct using the inverse check.
Add the difference back to the subtrahend.
433 + 391 should equal 824.
Correct: 433 + 391 = 824.
4. A child computes 50 - 23 = 33. What went wrong?
Check whether a borrow was taken.
0 - 3 cannot be done without regrouping.
The child subtracted 3 - 0 in the ones column instead of borrowing; the correct answer is 27.

📝 Topic test — 8 questions

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