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.

How to Do Long Subtraction

Step 1
Write the numbers you wish to subtract, one underneath the other.

Step 2
Look at the numbers in the right-most column.

Step 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.
Step 4
Move to the column to the left.

Step 5
Go to Step 3 and repeat until all columns have been subtracted.

A Real Example of How to Do Long Subtraction

Question: What is the answer to the subtraction below?:

Step 1
Write the numbers you wish to subtract, one underneath the other.

Step 2
Look at the numbers in the right-most column.

Step 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:

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, 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.

Step 4
Move to the column to the left.

Step 5
Go to Step 3.

Step 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:

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, 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.

Step 4 (1st repeat): Move to the column to the left.

Step 5 (1st repreat): Go to Step 3.

Step 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:

1 is larger than or equal to 1.

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

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

The solution to 246 - 158 is 88.

Another Real Example of How to Do Long Subtraction

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

The slider below shows another example of how to do long subtraction:
show

PARTS OF A SUBTRACTION

• The number you take away is the subtrahend.

• The result of subtracting the numbers is the difference.

DIGITS AND PLACE VALUE

Numbers consist of digits. In a decimal, the digits can take values 0 through to 9.

The value of the digits depend on its place value.

The place value is the place in the number where the digit is. Place values include hundreds, tens and units.

For example,

123 consists of:

• 1 hundred.
• 2 tens.
• 3 units.
That is:

Each place value is 10 times bigger than that to its right. A hundred is 10 times a ten, a ten is ten times a unit.

The same system applies to the right of the decimal place:

PLACE VALUE AND COLUMNS IN LONG SUBTRACTION

The columns in long addition correspond to the place values of the digits in the numbers to be subtracted.

This ensures that when you subtract the digits, they are of the same value - you are subtracting units from units and tens from tens.

PLACE VALUE AND BORROWING

In long subtraction, sometimes a larger digit is to be subtracted from a smaller digit:

7 is bigger than the 5 it is being taken away from.

Due to the place value system, any digit to the left of this column is 10 times bigger than a digit in the column.

In the top row, 5 is 5 units, but the 2 to its left is 2 tens. A ten can be borrowed from this column and added to the 5 units:

1 ten plus 5 units is 15.

Now, the 15 in the top row is bigger than the 7 in the bottom row, so the numbers can be subtracted:

Borrowing can be used whatever column is being subtracted, as digits to the left are always worth 10 of the digits in that column.

If the number on the top row in the tens column is not bigger than that below it, a hundred can be borrowed from the hundreds column to the left to make it bigger.

If the number on the top row in the hundreds column is not bigger than that below it, a thousand can be borrowed from the thousands column to the left to make it bigger.

Place value is the basis of borrowing in long subtraction.