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Decompose Fractions

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To decompose a given fraction into a sum of two, three, or four fractions, we first decompose it into unit fractions.

 

For example:

Let's decompose the fraction
5 6
into a sum of three fractions.

In order to do so, first let's decompose the given fraction into unit fractions.

 

17a

 

This model represents a whole divided into 6 equal parts. Here, each part represents the unit fraction
1 6
.
 

 

17b


 

The 5 shaded parts represent the fraction
5 6
.

 

17c


Now, write
5 6
as the sum of unit fractions.
5
6
=
1
6
+
1
6
+
1
6
+
1
6
+
1
6


The sum can also be written as:

5
6
=
1
6
+
1
6
+
1
6
+
1
6
+
1
6
       =
1
6
+
2
6
+
2
6

 

So,
5 6
can be written as a sum of three fractions as
1 6
+
2 6
+
2 6
.