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What is Long Division? - Definition & Examples

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  • 0:00 What Is Long Division?
  • 0:21 How to Perform Long Division
  • 1:59 Examples
  • 3:02 Lesson Summary
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Lesson Transcript
Instructor: Jennifer Beddoe
Long division is a method by which a person can perform more complex division problems using only a pencil and paper. This lesson will define long division, show how to perform the operation, and give some examples. There will be a quiz at the end to give you some practice.

What Is Long Division?

Long division is a mathematical operation which allows you to perform complicated division problems using pencil and paper. It breaks down the more complex problem into simpler steps. With the advances in computers and calculators, the need to know long division has faded. However, it is a good skill to have and an excellent way to exercise the brain.

How to Perform Long Division

A long division problem is not written as a fraction or like you might write a smaller problem. Problems that need to be worked out the long way are written out like this, with the dividend under the long division bracket, the divisor to the left of the bracket and the quotient on top of the bracket.

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The terms are the same; there is still a divisor, dividend and quotient, they are just are written in such a way to make it easier to calculate. In order to work out a long division problem, you first break it down into manageable division problems.

Let's look at the problem 965 / 5.

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You need to divide 5 into each of the numbers in 965.

  1. 5 will go in to 9 one time. 5 x 2 = 10, and that is too much, but 5 x 1 = 5, and that will work. Place a 1 above the 9 (above the line) then write a 5 under the 9. This is to show that 5 x 1 is 5.
  2. Subtract 5 from 9 to get 4 and then bring down the 6. 4 is the remainder from the first mini-division problem, and the 6 is the number you will use for the second mini-division problem.
  3. Now divide 5 into 46. 5 x 45 = 9, so 9 is the number we will write on top and then put 45 under the 46.
  4. 46 - 45 = 1, which makes 1 the remainder.
  5. Bring down the 5 to complete the final mini problem: 15 / 5 = 3
  6. Write a 3 above the 5, and 5 x 3 = 15.
  7. 15 - 15 = 0, there is no remainder and the problem is complete.

965 / 5 = 193

Examples

Let's go through some examples.

Example 1: 305,753 / 31

You can also work long division problems with very large numbers.

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For this example, 31 will not divide into 3, so you need to include the next number, 0. Since 31 also will not divide into 30 include the next number.

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