MathBored

Essential Math Primer
← Back to Primer Overview
K05 • Lesson 17 of 105

Multi-Digit Subtraction with Regrouping

Students learn to subtract two- and three-digit numbers using the standard algorithm, with a focus on regrouping (borrowing). Using base-10 blocks, they see why 1 ten can be broken into 10 ones when there aren't enough ones to subtract. They practice the written vertical method and use addition to check their answers, reinforcing the inverse relationship.

K-2 Foundations • K-2

Prerequisites: E03, K01, K02, K04

Key Concepts

  • vertical subtraction algorithm
  • regrouping a ten into ones when subtracting
  • regrouping a hundred into tens when subtracting
  • using addition to verify subtraction

Multi-Digit Subtraction with Regrouping

Subtraction takes away a smaller amount from a bigger one. Just like addition, we line up the numbers by place value and work from right to left. When a digit on top is smaller than the digit below it, we need to regroup (also called "borrowing").

Setting Up Vertical Subtraction

  1. Write the bigger number on top.
  2. Line up ones under ones, tens under tens, hundreds under hundreds.
  3. Subtract each column starting from the right (ones).

Worked Example 1: Subtracting Without Regrouping

Subtract 86 - 43.

  1. Ones: 6 - 3 = 3
  2. Tens: 8 - 4 = 4
86 - 43 = 43

When You Need to Regroup (Borrow)

If the top digit is smaller than the bottom digit, borrow 1 from the next column to the left. That borrowed 1 becomes 10 in the current column.

Worked Example 2: Two-Digit Subtraction with Regrouping

Subtract 52 - 28.

  1. Ones: 2 - 8? We cannot do that! Borrow 1 ten from the 5 tens. The 5 becomes 4, and the 2 becomes 12.
  2. Now ones: 12 - 8 = 4.
  3. Tens: 4 - 2 = 2.
  4 12
  5 2
- 2 8
------
  2 4

Answer: 24

Worked Example 3: Three-Digit Subtraction with Regrouping

Subtract 543 - 267.

  1. Ones: 3 - 7? Borrow from tens. Tens digit 4 becomes 3, ones become 13. Now: 13 - 7 = 6.
  2. Tens: 3 - 6? Borrow from hundreds. Hundreds digit 5 becomes 4, tens become 13. Now: 13 - 6 = 7.
  3. Hundreds: 4 - 2 = 2.
543 - 267 = 276

Checking with Addition

You can always check subtraction by adding! If 543 - 267 = 276, then 276 + 267 should equal 543.

276 + 267 = 543   (Check!)

Watch Out!

When you borrow, do not forget to reduce the digit you borrowed from by 1. If you borrow from the tens column, cross out the tens digit and write the new smaller number above it.

Real-World Connection

You have 52 crayons and give 28 to a friend. How many are left? 52 - 28 = 24 crayons. Subtraction helps us figure out what remains!

Practice Problems

1. Subtract: 75 - 31

Show Answer

75 - 31 = 44. No regrouping needed. Ones: 5-1=4. Tens: 7-3=4.

2. Subtract: 63 - 47

Show Answer

63 - 47 = 16. Ones: 3-7 requires borrowing. Borrow from 6, making it 5 and ones become 13. 13-7=6. Tens: 5-4=1.

3. Subtract: 400 - 156

Show Answer

400 - 156 = 244. We need to borrow twice: first the hundreds gives to the tens (making 10 tens), then the tens gives to ones. 10-6=4 ones, 9-5=4 tens, 3-1=2 hundreds.

4. Subtract 305 - 178, then check your answer with addition.

Show Answer

305 - 178 = 127. Check: 127 + 178 = 305. It works!

5. You had 250 marbles and lost 85. How many remain?

Show Answer

250 - 85 = 165 marbles. Ones: 0-5 borrow, 10-5=5. Tens: 4-8 borrow, 14-8=6. Hundreds: 1.

Lesson Summary

Overview