What Is Long Subtraction? (Interactive Widget)

Use this interactive widget to see a step-by-step explanation of long subtraction.

This is a randomly generated long-subtraction sum.

See similar widgets on long addition, long multiplication, and long division.

What Is Long Subtraction?

Long subtraction is a method for subtracting numbers. Long subtraction involves writing the numbers to be subtracted one underneath another, so the digits are in columns. The numbers are subtracted a column at a time.

Many numbers of any length (including decimals) can be subtracted in this way.

1

Write the numbers you wish to subtract, one underneath the other.

2

Look at the numbers in the right-most column.

3

Check if the number at the top of the column is larger than or equal to the number at the bottom of the column:

• If Yes, subtract the numbers, write the answer below the column (between the lines) and move to Step 4.

• If No, borrow a digit from the top number in the column to the left.

Cross out the top number on the column to the left, and write the number one less than it in its place..

Write a 1 in front of the top number in the column you are subtracting. The number will be 10 plus the number, which will be larger than the bottom number in the column.

Subtract the numbers, write the answer below the column (between the lines) and move to Step 4.

4

Move to the column to the left.

5

Go to Step 3 and repeat until all columns have been subtracted.

A Real Example of How to Do Long Subtraction

Doing long subtraction is easy.

Question

Subtract the numbers below. 1

Write the numbers you wish to subtract, one underneath the other. 2

Look at the numbers in the right-most column. 3

Check if the number at the top of the column is larger than or equal to the number at the bottom of the column:

No. 6 is not larger than or equal to 8.

• If No, borrow a digit from the top number in the column to the left.

Cross out the top number on the column to the left (4), and write the number one less (3) than it in its place. • Write a 1 in front of the top number in the column you are subtracting. The number will be 10 plus the number, which will be larger than the bottom number in the column. • Subtract the numbers, write the answer below the column (between the lines) and move to Step 4. 16 − 8 = 8

4

Move to the column to the left. Go to Step 3.

3

1st repeat

Check if the number at the top of the column is larger than or equal to the number at the bottom of the column:

No. 3 is not larger than or equal to 5.

• If No, borrow a digit from the top number in the column to the left.

Cross out the top number on the column to the left (2), and write the number one less (1) than it in its place. • Write a 1 in front of the top number in the column you are subtracting. The number will be 10 plus the number, which will be larger than the bottom number in the column. • Subtract the numbers, write the answer below the column (between the lines) and move to Step 4. 13 − 5 = 8

4

1st repeat

Move to the column to the left. 1st repeat

Go to Step 3.

3

2nd repeat

Check if the number at the top of the column is larger than or equal to the number at the bottom of the column:

Yes. 1 is larger than or equal to 1.

• If Yes, If Yes, subtract the numbers, write the answer below the column (between the lines). 1 − 1 = 0

There are no more columns to the left. All columns have been subtracted.

The solution to 246 − 158 is 88.

Slider

It is possible to subtract decimals from each other, as well as to subtract more than two numbers.

The slider below shows another real example of how to do long subtraction.

Open the slider in a new tab

How to subtract What is place value? Try a long subtraction ( interactive widget)