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High School Algebra I: Help and Review25 chapters | 292 lessons

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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.

**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.

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.

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.

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

- 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.
- 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.
- 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.
- 46 - 45 = 1, which makes 1 the remainder.
- Bring down the 5 to complete the final mini problem: 15 / 5 = 3
- Write a 3 above the 5, and 5 x 3 = 15.
- 15 - 15 = 0, there is no remainder and the problem is complete.

965 / 5 = 193

Let's go through some examples.

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

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.

305 / 31 is the first mini-division problem to work out. After that, the problem continues as usual. By the time you are done, we know that 305,753 / 31 = 9,863.

Long division problems don't always work out evenly. Sometimes, there will be a remainder.

The remainder can be written in two ways. The first is like in this example, 'R4' which tells you that there is a remainder of 4. The other way is a fraction with the remainder as the numerator and the divisor as the denominator. For this problem, that would be 4 / 7. Either way is correct.

**Long division** is a method for solving complex division problems without a calculator. All it takes is a piece of paper, a pencil, and some brain power. In order to work out a long division problem, you first break it down into manageable division problems. For problems that have a remainder, it can be written in one of two ways: 'R' plus the leftover number, or the leftover number as part of a fraction.

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High School Algebra I: Help and Review25 chapters | 292 lessons

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- Graphing Rational Numbers on a Number Line 5:02
- Notation for Rational Numbers, Fractions & Decimals 6:16
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