Question

student practice directions: decompose the fraction usin number line. 1. \\(\frac{4}{9} = \frac{\quad}{\quad} + \frac{\quad}{\quad}\\) \\(\frac{4}{5} = \frac{\quad}{\quad} + \frac{\quad}{\quad}\\)

Explanation:

Step1: Recall fraction decomposition

To decompose a fraction, we can express it as the sum of two fractions with the same denominator. For $\frac{4}{9}$, we can split the numerator 4 into two parts, say 1 and 3 (or other combinations like 2 and 2). So we can write $\frac{4}{9}=\frac{1}{9}+\frac{3}{9}$ (or $\frac{2}{9}+\frac{2}{9}$, etc.). Let's take the first combination.

Step2: Verify the sum

Check if $\frac{1}{9}+\frac{3}{9}=\frac{1 + 3}{9}=\frac{4}{9}$, which is correct.

Step1: Decompose the numerator

Split 4 into two parts, e.g., 1 and 3, or 2 and 2. Let's use 1 and 3. Then $\frac{4}{5}=\frac{1}{5}+\frac{3}{5}$.

Step2: Check the sum

$\frac{1}{5}+\frac{3}{5}=\frac{1 + 3}{5}=\frac{4}{5}$, which is correct.

Answer:

$\frac{4}{9}=\boldsymbol{\frac{1}{9}+\frac{3}{9}}$ (or other valid decompositions like $\frac{2}{9}+\frac{2}{9}$)

For the second fraction $\frac{4}{5}$: