Regrouping
Grade 4 students master regrouping (borrowing) in subtraction in Saxon Math Intermediate 4 Chapter 2. When the top digit in any column is smaller than the bottom digit, you must borrow 1 from the next column to the left: reduce that column's digit by 1 and add 10 to the current column. For 81 − 38: ones column 1 < 8 requires borrowing; 8 tens becomes 7, ones becomes 11; 11 − 8 = 3, 7 − 3 = 4; answer 43. The foundational rule: always subtract bottom from top, never swap the digits.
Key Concepts
Property When subtracting, if a digit in the top number is smaller than the digit below it, you must regroup. This means trading 1 from the next higher place value for 10 of the current place value.
Examples To solve $53 29$: Regroup 5 tens and 3 ones into 4 tens and 13 ones. Now you can subtract: $13 9=4$ in the ones place and $4 2=2$ in the tens place. The answer is 24. For $63 36$, you show regrouping like this: $$ \begin{array}{r} \cancel{6}^5\cancel{3}^{13} \\ 3\phantom{0}6 \\ \hline 2\phantom{0}7 \\ \end{array} $$.
Explanation You can't subtract 9 from 3! Regrouping is like trading a ten dollar bill for ten one dollar bills. You still have the same total value, but now you have enough ones to subtract from.
Common Questions
What is regrouping (borrowing) in subtraction?
Regrouping means trading 1 unit from the next larger place value for 10 of the current place value, when the top digit is smaller than the bottom digit. The total value does not change—only the distribution between columns shifts.
How do you solve 81 − 38 using regrouping?
Ones: 1 < 8, so borrow. Tens digit 8 becomes 7; ones digit 1 becomes 11. Ones: 11 − 8 = 3. Tens: 7 − 3 = 4. Answer: 43.
How do you know when regrouping is required?
Look at the ones column first. If the top digit is smaller than the bottom digit, you must regroup. Then check the tens column after regrouping, since borrowing reduced the tens digit and may create another situation requiring regrouping.
What is the critical rule you must never break in subtraction?
Always subtract the bottom number from the top number. Never flip the digits in a column (doing 8−1 instead of regrouping to get 11−8). Swapping gives a wrong answer that looks superficially plausible.
How is subtraction regrouping like borrowing money?
If you need to spend $9 but only have a $5 bill and three $1 bills, you trade a $10 bill for ten $1 bills first. In subtraction, you trade 1 ten for 10 ones before you can subtract in the ones column.
Can you need to regroup from the hundreds column in a three-digit subtraction problem?
Yes. After borrowing from the tens column reduces the tens digit, the tens column may now need to borrow from the hundreds column. Apply the same rule: reduce the next column by 1 and add 10 to the current column.