Subtraction: Regrouping, Zeros, and Checking Answers

Subtraction takes one number away from another to find the difference. This page covers place value, regrouping (borrowing), subtracting across zeros, checking your answer with addition, and practice.

What are the parts of a subtraction problem?

Subtraction is the arithmetic operation where one number, the subtrahend, is taken away from another number, the minuend, to leave the difference (Britannica).

In 705 − 295, 705 is the minuend, 295 is the subtrahend, and the difference is the answer. Subtraction is the inverse of addition. That’s the idea behind checking a subtraction problem, covered further down this page.

This section covers the basic vocabulary only. It doesn’t cover subtracting negative numbers, which flips some of these rules and comes up later in math.

Why does place value matter in subtraction?

Place value is the idea that a digit’s position tells you its value, ones, tens, hundreds, and so on. To subtract multi-digit numbers, you line up the digits by place value first, ones under ones, tens under tens, hundreds under hundreds.

In the number 705, the 7 is in the hundreds place, the 0 is in the tens place, and the 5 is in the ones place. Getting these lined up correctly is what makes column subtraction work.

This section covers whole-number place value. It doesn’t cover decimal place value, which lines up around a decimal point instead, as covered on our decimals page.

How does regrouping (borrowing) work?

Regrouping, also called borrowing, is what you do when a digit in the minuend is smaller than the digit below it in the subtrahend. You take 10 from the next column over and add it to the smaller digit, so you can subtract.

Worked example. Subtract 187 from 523.

1. Ones column: 3 − 7. Since 3 is smaller than 7, regroup. Take 1 ten from the tens column, making it 10 extra ones: 13 − 7 = 6.
2. Tens column: the tens digit dropped from 2 to 1 after regrouping. Now subtract: 1 − 8. Since 1 is smaller than 8, regroup again. Take 1 hundred from the hundreds column, making it 10 extra tens: 11 − 8 = 3.
3. Hundreds column: the hundreds digit dropped from 5 to 4 after regrouping. Now subtract: 4 − 1 = 3.

Reading the columns hundreds, tens, ones gives 336. So 523 − 187 = 336.

This section covers regrouping across three-digit numbers. It doesn’t cover regrouping with decimals, which uses the same idea across the decimal point.

How do you subtract when the minuend has zeros?

Subtracting across zeros needs an extra regrouping step, because you can’t take 10 from a column that’s already a zero. You have to regroup from further left first.

Worked example. Subtract 247 from 500.

1. Ones column: 0 − 7. The tens column is also 0, so you can’t regroup from it directly. Regroup from the hundreds column instead: take 1 hundred from the 5, leaving 4 hundreds, and turn it into 10 tens in the tens column.
2. Now the tens column has 10. Take 1 ten from it for the ones column, leaving 9 tens, and turn it into 10 extra ones: 10 − 7 = 3.
3. Tens column: 9 − 4 = 5.
4. Hundreds column: 4 − 2 = 2.

Reading the columns gives 253. So 500 − 247 = 253.

This section covers subtracting across one or more zeros in whole numbers. It doesn’t cover subtracting across zeros in decimals, which follows the same regrouping chain.

How do you check a subtraction answer?

Since subtraction is the inverse of addition, you can check any subtraction problem by adding the difference back to the subtrahend. The result should equal the original minuend.

Checking example. Check that 705 − 295 = 410. Add the difference to the subtrahend: 410 + 295 = 705. That matches the original minuend, so the answer is correct.

This section covers checking whole-number subtraction. It doesn’t cover checking subtraction of fractions or decimals, which uses the same idea but needs matching parts first.

Practice set

Work through these on paper, then check your answers.

1. 83 − 29
2. 400 − 156
3. 721 − 458
4. 1000 − 463
5. 6005 − 2318

Subtraction and division both build on the same place-value ideas as addition, just running in reverse. Once regrouping feels automatic, it carries straight over into subtracting fractions and into subtraction steps inside word problems. For more topics, visit our math hub.

Sources

• Britannica. Subtraction.