How to Decompose Fractions: Lesson for Kids

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  • 0:04 What Is a Fraction?
  • 1:02 Decomposing Fractions
  • 2:28 One Last Example
  • 3:28 Lesson Summary
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Lesson Transcript
Instructor: Nick Rogers
Fraction decomposition is a technique used for breaking fractions into smaller components. This lesson helps you become more comfortable with how to decompose a fraction as well as offering some visual aids.

What Is a Fraction?

Fractions have been important in math almost as long as the subject has existed. The ancient Greek mathematician Pythagoras believed that every number could be written as a fraction. He found beauty in different fractions and took joy in reducing them to their most basic form.

A fraction has a numerator and a denominator. We write a fraction with the numerator on the top and the denominator on the bottom. Fractions are divisions of a whole. When we decompose a fraction, we break it into parts. There are many ways to think about breaking fractions apart. Sometimes, it's convenient to write a fraction in a less simple form to help with our understanding.

It is perfectly valid to write any of the following, since they each mean the same:

  • 3/8
  • 1/8 + 1/8 + 1/8
  • 3 x (1/8)

You should try to become comfortable with all of these expressions and understand when it is useful to replace multiplication with addition. The process of converting 3/8 to 1/8 + 1/8 + 1/8 is called decomposition, and it is the subject of today's lesson.

Decomposing Fractions

Decomposing a fraction means breaking it into pieces. As a simple example, we could decompose 4/8 as follows:

4/8 = 1/8 + 1/8 + 1/8 + 1/8

Of course, this isn't really that exciting because 4/8 was already fairly easy to understand. Four is half of eight, so therefore:

4/8 = 1/2

When the numerator is larger than the denominator, decomposing a fraction can be very useful. Consider the fraction 5/4. We could decompose this fraction into one part smaller than one and one part larger so that we can see how much bigger than one the fraction is.

Now, let's try to decompose 2 2/7 into its component pieces. We can break up both the whole part and fractional part using two steps. First, express 2 as 1 + 1. Then understand that, in this instance, 1 = 7/7.

So to decompose 2 2/7, we would have the following:

= 1 + 1 + 1/7 + 1/7

= 7/7 + 7/7 + 1/7 +1/7

In this way, we have broken 2 2/7 into fractions that all have a common denominator. This will be very useful when you want to add fractions together.

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