# Decomposing fractions review

CCSS Math: 4.NF.B.3b
Review the basics of decomposing fractions, and try some practice problems.

## Decomposing fractions

To decompose a number, we break it into smaller parts.
We can decompose $54$ into $50+4$.
Fractions, like all numbers, can be decomposed in many ways.
Here are a few possible ways to decompose $7$ :
• $2+5$
• $4+2+1$
• $6+1$
• $1+2+3+1$

### Example 1: Tape diagram

Let's decompose $\dfrac59$.
One way we can decompose $\dfrac59$ is $\goldD{\dfrac29}+\greenD{\dfrac39}$:
$\goldD{\dfrac29}+\greenD{\dfrac39}=\dfrac{\goldD2+\greenD3}9=\dfrac59$
Another way we can decompose $\dfrac59$ is $\purpleD{\dfrac19}+\redD{\dfrac29}+\tealD{\dfrac29}$:
$\purpleD{\dfrac19}+\redD{\dfrac29}+\tealD{\dfrac29}=\dfrac{\purpleD1+\redD2+\tealD2}9=\dfrac59$

### Example 2: Number line

How can we decompose $\dfrac64$?
One way we can decompose $\dfrac64$ is $\purpleD{\dfrac14}+\purpleD{\dfrac14}+\purpleD{\dfrac14}+\purpleD{\dfrac14}+\purpleD{\dfrac14}+\purpleD{\dfrac14}$:
$\purpleD{\dfrac14}+\purpleD{\dfrac14}+\purpleD{\dfrac14}+\purpleD{\dfrac14}+\purpleD{\dfrac14}+\purpleD{\dfrac14}=\dfrac{\purple1+\purple1+\purple1+\purple1+\purple1+\purple1}4=\dfrac64$
Another way we can decompose $\dfrac64$ is $\blueD{\dfrac34}+\blueD{\dfrac34}$:
$\blueD{\dfrac34}+\blueD{\dfrac34}=\dfrac{\blueD3+\blueD3}4=\dfrac64$
Which of these sums equal $\dfrac{14}{10}$ ?