Question

decompose the fractions below two different ways.
\frac{15}{7} \square + \square =
or \square + \square =
\frac{8}{3} \square + \square =
or \square + \square =
subtract the fractions below and put difference in the simplest form.

Explanation:

Step1: Decompose $\frac{15}{7}$ (Way 1)

We can split the numerator 15 into two parts. Let's take 7 and 8. So, $\frac{15}{7}=\frac{7}{7}+\frac{8}{7}$. Since $\frac{7}{7} = 1$, this is a valid decomposition.

Step2: Decompose $\frac{15}{7}$ (Way 2)

Another way: split 15 into 14 and 1. Then $\frac{15}{7}=\frac{14}{7}+\frac{1}{7}$. And $\frac{14}{7}=2$, so this works too.

Step3: Decompose $\frac{8}{3}$ (Way 1)

Split 8 into 3 and 5. So, $\frac{8}{3}=\frac{3}{3}+\frac{5}{3}$. $\frac{3}{3}=1$, which is valid.

Step4: Decompose $\frac{8}{3}$ (Way 2)

Split 8 into 6 and 2. Then $\frac{8}{3}=\frac{6}{3}+\frac{2}{3}$. $\frac{6}{3}=2$, so this is also valid.

Answer:

For $\frac{15}{7}$: $\frac{7}{7}+\frac{8}{7}=\frac{15}{7}$ or $\frac{14}{7}+\frac{1}{7}=\frac{15}{7}$ (other valid decompositions like $\frac{1}{7}+\frac{14}{7}$, $\frac{8}{7}+\frac{7}{7}$ etc. are also acceptable)
For $\frac{8}{3}$: $\frac{3}{3}+\frac{5}{3}=\frac{8}{3}$ or $\frac{6}{3}+\frac{2}{3}=\frac{8}{3}$ (other valid decompositions like $\frac{5}{3}+\frac{3}{3}$, $\frac{2}{3}+\frac{6}{3}$ etc. are also acceptable)