Subtracting Two-Digit Numbers with Regrouping
Grade 4 students practice subtracting two-digit numbers with regrouping in Saxon Math Intermediate 4 Chapter 2. Regrouping (also called borrowing or exchanging) means trading one ten for ten ones when the top digit in the ones column is smaller than the bottom digit. In 52 − 28: the ones column shows 2 − 8 is impossible, so borrow 1 ten from the 5, making it 4 tens and 12 ones; then 12 − 8 = 4 and 4 − 2 = 2, giving 24. The critical warning: never subtract the smaller from the larger regardless of position.
Key Concepts
New Concept Trading 1 ten for 10 ones is an example of regrouping , or exchanging .
What’s next Next, you'll use money manipulatives and drawings to practice regrouping, then solve subtraction problems using pencil and paper.
Common Questions
What is regrouping in subtraction?
Regrouping means trading one unit from the next higher place value for ten of the current place value. For example, if you cannot subtract in the ones column, you take 1 ten from the tens column and convert it to 10 ones.
How do you subtract 52 minus 28 using regrouping?
Ones: 2 − 8 is impossible. Borrow 1 ten from the 5 tens (which becomes 4). Add 10 to the ones: 10 + 2 = 12. Now 12 − 8 = 4. Tens: 4 − 2 = 2. Answer: 24.
Why must you never subtract the smaller digit from the larger digit regardless of position?
Subtraction always goes top minus bottom. If the top digit is smaller, you must regroup. Flipping the subtraction (doing 8 − 2 instead of regrouping to get 12 − 8) gives the wrong answer.
How is regrouping like trading money?
If you need to give someone $8 but only have a $20 bill, you trade the $20 for twenty $1 bills first. In the same way, when you cannot subtract in the ones column, you trade 1 ten for 10 ones to get enough ones to subtract from.
How do you know when regrouping is required?
Look at the ones column first. If the top digit is smaller than the bottom digit (like 2 − 8), you must regroup before subtracting. If the top digit is larger or equal, no regrouping is needed.
Can you need to regroup from the hundreds column?
Yes. In multi-digit subtraction, if the tens column also needs regrouping after you regroup from hundreds, you apply the same process: trade 1 hundred for 10 tens and continue subtracting column by column.