1/15
00:00

Learn more about this topic →

I.2 Subtract two numbers up to four digits

Loading questions...

Go to the practice →

What is subtraction?

Subtraction is a mathematical operation that finds the difference between two numbers. When we subtract, we take away one quantity from another to find out how much is left.

Example:
8
- 3
5

We start with 8 items, take away 3 items, and have 5 items left.

Note

In subtraction, the first number is called the minuend, and the second number is called the subtrahend. The answer is called the difference.

Subtracting without regrouping

When subtracting without regrouping, each digit in the top number is larger than the digit directly below it, so we don't need to borrow from neighboring place values.

Example:
4,857
- 1,325
3,532

Step-by-step process:

  1. Start with the ones place: 7 - 5 = 2
  2. Move to the tens place: 5 - 2 = 3
  3. Move to the hundreds place: 8 - 3 = 5
  4. Move to the thousands place: 4 - 1 = 3
Note

Always start subtracting from the rightmost digit (ones place) and move left to the thousands place.

Subtracting with regrouping in the ones place

When the digit in the ones place of the top number is smaller than the digit below it, we need to regroup from the tens place.

Example:
32
- 17
15

Step-by-step process:

  1. Look at the ones place: 2 - 7 (can't do)
  2. Regroup 1 ten from the tens place (3 becomes 2)
  3. Add the regrouped ten to the ones place (2 becomes 12)
  4. Subtract ones: 12 - 7 = 5
  5. Subtract tens: 2 - 1 = 1
Note

When regrouping, remember to reduce the digit you borrowed from by 1 and add 10 to the digit you're working with.

Subtracting with regrouping in the tens place

When the digit in the tens place of the top number is smaller than the digit below it, we need to regroup from the hundreds place.

Example:
546
- 187
359

Step-by-step process:

  1. Look at the ones place: 6 - 7 (can't do)
  2. Regroup from tens: 2 tens becomes 1 ten, ones become 16
  3. Subtract ones: 16 - 7 = 9
  4. Look at tens: 1 - 8 (can't do)
  5. Regroup from hundreds: 4 hundreds becomes 3 hundreds, tens become 11
  6. Subtract tens: 11 - 8 = 3
  7. Subtract hundreds: 3 - 1 = 2
Note

Sometimes you need to regroup multiple times in the same problem. Work carefully from right to left.

Subtracting with regrouping in the hundreds place

When the digit in the hundreds place of the top number is smaller than the digit below it, we need to regroup from the thousands place.

Example:
3,445
- 1,687
1,758

Step-by-step process:

  1. Look at the ones place: 5 - 7 (can't do)
  2. Regroup from tens: 2 tens becomes 1 ten, ones become 15
  3. Subtract ones: 15 - 7 = 8
  4. Look at tens: 1 - 8 (can't do)
  5. Regroup from hundreds: 4 hundreds becomes 3 hundreds, tens become 11
  6. Subtract tens: 11 - 8 = 3
  7. Look at hundreds: 3 - 6 (can't do)
  8. Regroup from thousands: 3 thousands becomes 2 thousands, hundreds become 13
  9. Subtract hundreds: 13 - 6 = 7
  10. Subtract thousands: 2 - 1 = 1
Note

When regrouping across multiple places, it's helpful to write small numbers above the digits to keep track of your changes.

Subtracting across zeros

When you need to subtract and encounter zeros in the top number, you may need to regroup across multiple place values at once.

Example:
4,000
- 1,275
2,725

Step-by-step process:

  1. Look at the ones place: 0 - 5 (can't do)
  2. Regroup from tens: 0 tens (can't do)
  3. Regroup from hundreds: 0 hundreds (can't do)
  4. Regroup from thousands: 4 thousands becomes 3 thousands, hundreds become 10
  5. Regroup from hundreds: 10 hundreds becomes 9 hundreds, tens become 10
  6. Regroup from tens: 10 tens becomes 9 tens, ones become 10
  7. Subtract ones: 10 - 5 = 5
  8. Subtract tens: 9 - 7 = 2
  9. Subtract hundreds: 9 - 2 = 7
  10. Subtract thousands: 3 - 1 = 2
Note

When subtracting across zeros, you may need to "borrow" from several places away. Think of it as a chain reaction moving from left to right.

Checking your subtraction

You can verify your subtraction answer is correct by using addition. Add your answer (difference) to the number you subtracted (subtrahend). The sum should equal the original number (minuend).

Example:

If 4,283 - 1,759 = 2,524, then:

2,524
+ 1,759
4,283

Since 2,524 + 1,759 = 4,283, our subtraction was correct.

Note

Always check your work! This helps catch mistakes and builds confidence in your subtraction skills.

Go to the practice →