Question

2
\\(\frac{8}{13} \div \frac{1}{8} = \frac{\square}{\square} = \square \frac{\square}{\square}\\)
\\(\frac{1}{7} \div \frac{2}{15} = \frac{\square}{\square} = \square \frac{\square}{\square}\\)

Explanation:

First Problem: $\boldsymbol{\frac{8}{13} \div \frac{1}{8}}$

Step1: Recall fraction division rule

To divide a fraction by another fraction, multiply the first fraction by the reciprocal of the second fraction. So, $\frac{8}{13} \div \frac{1}{8} = \frac{8}{13} \times 8$.

Step2: Multiply the numerators and denominators

Multiplying the numerators: $8 \times 8 = 64$. The denominator remains $13$. So, $\frac{8}{13} \times 8 = \frac{64}{13}$.

Step3: Convert improper fraction to mixed number

Divide $64$ by $13$. $13 \times 4 = 52$, and $64 - 52 = 12$. So, $\frac{64}{13} = 4\frac{12}{13}$.

Second Problem: $\boldsymbol{\frac{1}{7} \div \frac{2}{15}}$

Step1: Recall fraction division rule

Multiply the first fraction by the reciprocal of the second fraction. So, $\frac{1}{7} \div \frac{2}{15} = \frac{1}{7} \times \frac{15}{2}$.

Step2: Multiply the numerators and denominators

Multiplying the numerators: $1 \times 15 = 15$. Multiplying the denominators: $7 \times 2 = 14$. So, $\frac{1}{7} \times \frac{15}{2} = \frac{15}{14}$.

Step3: Convert improper fraction to mixed number

Divide $15$ by $14$. $14 \times 1 = 14$, and $15 - 14 = 1$. So, $\frac{15}{14} = 1\frac{1}{14}$.

Answer:

For $\frac{8}{13} \div \frac{1}{8}$: $\frac{64}{13}$, $4\frac{12}{13}$
For $\frac{1}{7} \div \frac{2}{15}$: $\frac{15}{14}$, $1\frac{1}{14}$