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Lesson 1: Decomposing fractions

# Decomposing fractions review

Review the basics of decomposing fractions, and try some practice problems.

## Decomposing fractions

To decompose a number, we break it into smaller parts.
Fractions, like all numbers, can be decomposed in many ways.

### Example 1: Tape diagram

Let's decompose $\frac{5}{9}$.
One way we can decompose $\frac{5}{9}$ is $\frac{2}{9}+\frac{3}{9}$:
$\frac{2}{9}+\frac{3}{9}=\frac{2+3}{9}=\frac{5}{9}$
Another way we can decompose $\frac{5}{9}$ is $\frac{1}{9}+\frac{2}{9}+\frac{2}{9}$:
$\frac{1}{9}+\frac{2}{9}+\frac{2}{9}=\frac{1+2+2}{9}=\frac{5}{9}$

### Example 2: Number line

How can we decompose $\frac{6}{4}$?
One way we can decompose $\frac{6}{4}$ is $\frac{1}{4}+\frac{1}{4}+\frac{1}{4}+\frac{1}{4}+\frac{1}{4}+\frac{1}{4}$:
$\frac{1}{4}+\frac{1}{4}+\frac{1}{4}+\frac{1}{4}+\frac{1}{4}+\frac{1}{4}=\frac{1+1+1+1+1+1}{4}=\frac{6}{4}$
Another way we can decompose $\frac{6}{4}$ is $\frac{3}{4}+\frac{3}{4}$:
$\frac{3}{4}+\frac{3}{4}=\frac{3+3}{4}=\frac{6}{4}$
Which of these sums equal $\frac{14}{10}$ ?