Questions: Two-Digit Subtraction With Regrouping

Question 1

A student computes 42 − 17. In the ones column, she tries to subtract 7 from 2 and gets stuck. What should she do?

• A. Write a negative number in the ones column and continue
• B. Skip the ones column and subtract only the tens: 4 − 1 = 3, so the answer is 30
• C. Regroup: borrow 1 ten from the tens column, making the ones column 12, then subtract 12 − 7 = 5
• D. Round both numbers before subtracting to avoid the problem

Answer: (C)

When the ones digit being subtracted is larger than the ones digit in the number, you must regroup. You borrow 1 ten from the tens column (reducing 4 tens to 3 tens) and add it to the ones column as 10 ones (making 2 + 10 = 12 ones). Then 12 − 7 = 5 ones, and 3 − 1 = 2 tens, giving 25. Skipping columns or getting a negative ones digit would produce wrong answers.

Question 2

A student is computing 53 − 28. After regrouping, what does the number 53 become?

• A. 4 tens and 13 ones — the total is still 53
• B. 4 tens and 3 ones — the total is now 43
• C. 5 tens and 13 ones — you added ones without changing tens
• D. 3 tens and 13 ones — you borrowed two tens

Answer: (A)

Regrouping converts 53 into 4 tens + 13 ones. You take 1 ten from the tens column (reducing 5 to 4), and give it to the ones column as 10 ones (adding 10 to 3 to make 13). The total value stays at 53: 4 × 10 + 13 = 40 + 13 = 53. This is the key insight: regrouping rearranges the representation without changing the value. Option B incorrectly subtracts from the total; option C doesn't reduce the tens; option D takes two tens.

Question 3

When you regroup in 32 − 15, the value of 32 changes to 22 because you took away one of the tens.

• T. True
• F. False

Answer: False

This is the most important conceptual point about regrouping: it does not change the value of the number. After regrouping, 32 is represented as 2 tens + 12 ones instead of 3 tens + 2 ones, but 2 × 10 + 12 = 32 either way. You have not removed anything from the number — you have only changed how it is arranged. If students think the value changed, they will add or subtract incorrectly in the tens column.

Question 4

In the problem 41 − 18, you cannot subtract the ones column without regrouping.

• T. True
• F. False

Answer: True

In 41 − 18, the ones column asks you to subtract 8 from 1. Since 8 > 1, you cannot do this without going negative, so regrouping is required. You borrow 1 ten from the tens column (reducing 4 to 3) and add it to the ones (making 11), then compute 11 − 8 = 3 ones and 3 − 1 = 2 tens, giving 23. Whenever the ones digit being subtracted is larger than the ones digit in the top number, regrouping is necessary.

Question 5

Why must you cross out the tens digit and write a smaller number after you regroup? What happens if you forget this step?

Model answer: When you borrow a ten, that ten moves to the ones column — it no longer belongs to the tens column. If you don't reduce the tens digit, you're counting that ten twice: once in the ones column (where you added it) and once in the tens column (where you left it). This secretly adds 10 to your number and makes the final answer wrong.

Forgetting to reduce the tens digit is the most common regrouping error. For example, in 32 − 15, if you regroup to get 12 ones but leave the tens as 3 instead of writing 2, you will compute 2 − 1 = 1 ten and record 17 — the correct answer. But if you leave it as 3, you'll compute 3 − 1 = 2 tens, giving 27, which is wrong. The act of crossing out the old tens digit and writing the new one is the record-keeping step that prevents double-counting.