Question

$\frac{6}{8} \div \frac{3}{9} =$

1. $\frac{3}{7} \div \frac{5}{12} =$

Explanation:

First Problem: $\boldsymbol{\frac{6}{8} \div \frac{3}{9}}$

Step1: Recall division of fractions rule

To divide fractions, multiply by the reciprocal: $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$. So, $\frac{6}{8} \div \frac{3}{9} = \frac{6}{8} \times \frac{9}{3}$.

Step2: Simplify and multiply

Simplify $\frac{9}{3}=3$ and $\frac{6}{8}=\frac{3}{4}$. Then multiply: $\frac{3}{4} \times 3 = \frac{9}{4}$.

Step1: Apply fraction division rule

Using $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$, we get $\frac{3}{7} \div \frac{5}{12} = \frac{3}{7} \times \frac{12}{5}$.

Step2: Multiply numerators and denominators

Multiply numerators: $3 \times 12 = 36$; multiply denominators: $7 \times 5 = 35$. So, $\frac{36}{35}$.

Answer:

$\frac{9}{4}$ (or $2\frac{1}{4}$)

Second Problem: $\boldsymbol{\frac{3}{7} \div \frac{5}{12}}$