Questions: Three-Digit Subtraction With Regrouping

Question 1

You are solving 425 - 167. In the ones column, 5 - 7 is not possible. What is the correct first step?

• A. Write 0 in the ones column and move on to the tens
• B. Subtract 5 from 7 instead, giving 2, and write 2 in the ones column
• C. Regroup: borrow 1 ten from the tens column, making the ones column 15 - 7
• D. Start with the hundreds column first since the ones column has a problem

Answer: (C)

When the top digit in a column is smaller than the bottom digit, you regroup (borrow) from the next column. Take 1 ten from the tens place, reducing the tens digit from 2 to 1 and increasing the ones column from 5 to 15. Now 15 - 7 = 8. Option A (writing 0 and skipping) is wrong. Option B reverses the subtraction — subtracting 5 from 7 instead of 7 from 15 — a very common error that produces an incorrect result.

Question 2

What must you do when you need to regroup in the ones column but the tens digit of the top number is 0?

• A. Write 0 in the tens place and borrow from the ones column instead
• B. Skip that step and only regroup in the hundreds column
• C. First borrow from the hundreds to give the tens column something to lend, then borrow from the tens
• D. The problem cannot be solved when a 0 appears in the tens place

Answer: (C)

A 0 in the tens column means you can't borrow from it directly — it's empty. The solution is a two-step trade: borrow 1 hundred from the hundreds column, which turns 0 tens into 10 tens. Now take 1 of those 10 tens for the ones column (giving 10 additional ones), leaving 9 tens. This is the trickiest regrouping case, but the logic is the same: you're trading across two columns instead of one.

Question 3

Regrouping in subtraction changes the total value of the number you are subtracting from.

• T. True
• F. False

Answer: False

Regrouping never changes the value of the number — it only changes how that value is written in place-value columns. For example, 325 can be written as 3 hundreds + 2 tens + 5 ones, or equivalently as 3 hundreds + 1 ten + 15 ones. Both represent exactly 325. You are renaming the number in a different form to make column subtraction possible, not adding or removing any quantity.

Question 4

When you 'borrow' a ten during subtraction, you is expected to remember to pay it back at the end of the problem.

• T. True
• F. False

Answer: False

Nothing is actually borrowed or paid back — this is why the word 'borrow' is misleading. Regrouping renames the number: trading 1 ten for 10 ones changes how the digits appear in each column, but the total value is identical before and after. Once you've regrouped, the subtraction proceeds normally. There is no separate 'payback' step. The word 'regroup' or 'trade' describes the operation more accurately than 'borrow.'

Question 5

Explain why regrouping is sometimes called 'renaming' rather than 'borrowing,' and what stays the same during a regroup.

Model answer: Regrouping is 'renaming' because you rewrite the number in an equivalent form — changing 3 hundreds + 2 tens into 3 hundreds + 1 ten + 10 ones, for example. The total quantity (325) doesn't change, only how it's expressed in columns. Unlike 'borrowing,' nothing needs to be repaid — the new form is just as valid as the original.

Students who understand regrouping as renaming are much less likely to make procedural errors (like forgetting to reduce the tens digit after borrowing) because they understand WHY each step happens. The concept of equivalent representations — that 325 = 300 + 20 + 5 = 300 + 10 + 15 — is foundational to place-value understanding.