Question

use addition to decompose the fraction shown in the picture. you may write an equation or draw a model.

Explanation:

Step1: Analyze the fraction model

Assume the rectangle is divided into 5 equal parts, and 4 parts are shaded (blue). So the fraction is $\frac{4}{5}$. We can decompose it into the sum of unit fractions or other fractions. Let's use unit fractions: each part is $\frac{1}{5}$.

Step2: Decompose the fraction

$\frac{4}{5}$ can be written as the sum of four $\frac{1}{5}$s. So the equation is $\frac{1}{5} + \frac{1}{5} + \frac{1}{5} + \frac{1}{5} = \frac{4}{5}$. (Alternatively, we could also decompose it as $\frac{2}{5} + \frac{2}{5} = \frac{4}{5}$ or other combinations, but using unit fractions is a common way for decomposition.)

Answer:

$\frac{1}{5} + \frac{1}{5} + \frac{1}{5} + \frac{1}{5} = \frac{4}{5}$ (or other valid decompositions like $\frac{2}{5} + \frac{2}{5} = \frac{4}{5}$)