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How to Do Long Division (Mathematics Lesson)

What Is Long Division?

Long division is a method for dividing numbers.

How to Do Long Division

General Approach:

  • Identify the dividend and the divisor:



  • Write the dividend and divisor as follows:



  • Divide the first digit of the dividend (1) by the divisor (6), and write the whole number answer above the line. (Note: do not count remainders.)
    1 ÷ 6 = 0.


  • Multiply the answer from the previous operation (0) with the divisor (6). Write the result underneath the number divided into.
    0 × 6 = 0.



  • Subtract the bottom number from the top number.
    1 - 0 = 1.


  • Bring down the next digit of the dividend (3).


  • Divide this number (13) by the divisor (6), and write the whole number answer above the line. (Note: do not count remainders.)
    13 ÷ 6 = 2.




  • Multiply the answer from the previous operation (2) with the divisor (6). Write the result underneath the number divided into.
    2 × 6 = 12.



  • Subtract the bottom number from the top number.
    13 - 12 = 1.


  • Bring down the next digit of the dividend (8).



  • Divide this number (18) by the divisor (6), and write the whole number answer above the line. (Note: do not count remainders.)
    18 ÷ 6 = 3.

There are no more digits to bring down, and 6 divided into 18 exactly, with no remainder.

The solution to 138 ÷ 6 is 23.

Another Real Example of How to Do Long Division

In the previous example, the numbers divided exactly, with no remainder. In this example, the numbers do not divide exactly, and there will be a remainder.

Also, in this example, the divisor has more than one digit.

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


  • Identify the dividend and the divisor.



  • Write the dividend and divisor as follows:



  • The divisor has two digits. Therefore, divide the first two digits of the dividend (20) by the divisor (12), and write the whole number answer above the line. (Note: do not count remainders.)
    20 ÷ 12 = 1.


    Note: Make sure to write the 1 above the 0 in 20. By place value, 1 is a unit, and the 0 is the unit in 20.


  • Multiply the answer from the previous operation (1) with the divisor (12). Write the result underneath the number divided into.
    1 × 12 = 12.



  • Subtract the bottom number from the top number.
    20 - 12 = 8.



  • Bring down the next digit of the dividend (0).



  • Divide this number (80) by the divisor (12), and write the whole number answer above the line. (Note: do not count remainders.)
    80 ÷ 12 = 6.



  • Multiply the answer from the previous operation (6) with the divisor (12). Write the result underneath the number divided into.
    6 × 12 = 72.



  • Subtract the bottom number from the top number.
    80 - 72 = 8.

All the digits have been brought down.

The solution to 200 ÷ 12 is 16 remainder 8.

Expressing a Division As a Decimal Not a Remainder

When one number does not divide exactly into another, it is possible to express the quotient as a decimal rather than as a whole number and a remainder.

The slider below shows an example of how to do long division, expressing the result as a decimal:
It is also possible to divide into, and divide by decimals:

How to do long division with decimals
Interactive Widget
Here is an interactive widget to help you learn about long division.
Quick Test
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Note

PARTS OF A DIVISION



  • The number you divide is the dividend.

  • The number you divide by is the divisor.

  • The result of the division is the quotient.

DIVISION AS THE OPPOSITE OF MULTIPLICATION

Division is the opposite, or inverse, of multiplication.

If:



then:



and:



If two factors multiply to a product, then the product divides by one factor to the other factor.

Top Tip

SHORT CUT FOR LONG DIVISION

When you gain enough confidence, you will notice that the first few step shown left are not necessary.

On the left, 1 is divided by 6. But 1 is smaller than 6, and so won't divide at least once. That is why 0 was written above.

Instead, don't divide by the first digit of the dividend, but move along the digits, left to right, until you find the first number larger than the divisor.



Just remember that the answer must be written above the last digit. The 2 must be written above the 3 in 13, not the 1.

Note

REMAINDERS

Division doesn't always work out perfectly. Numbers do not always divide into equal groups.

For example, what is:



Think about sharing 7 apples out into 2 equal groups:



Looking above, it can be seen that this is not possible to split the apples into 2 equal groups.

2 groups of 3 apples can be made, with 1 apple left over:



The answer to 7 ÷ 2 is 3 (as there are 3 apples in each group) remainder 1 (there is 1 apple left over).

This can be written as:



The r stands for remainder.

USING THE CALCULATOR

To use the calculator to find that 7 ÷ 2 = 3 r 1:

  • Press 7 ÷ 2 =

  • The answer is 3.5

  • Round the number down: 3 is the whole number answer.

  • Multiply the whole number answer by the divisor.
    3 × 2 = 6

  • Subtract this this from the dividend.
    7 - 6 = 1

    1 is the remainder.