Question

gebra find each quotient. write in simplest form.

1. $\frac{a}{7} div \frac{a}{42}$
2. $\frac{10}{3x} div \frac{5}{2x}$
3. $\frac{c}{8} div \frac{cd}{5}$

Explanation:

Step1: Rewrite division as multiplication

For $\frac{a}{7} \div \frac{a}{42}$:
$\frac{a}{7} \times \frac{42}{a}$

Step2: Simplify the expression

Cancel common factors $a$, then compute $\frac{42}{7}$:
$\frac{42}{7} = 6$

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Step1: Rewrite division as multiplication

For $\frac{10}{3x} \div \frac{5}{2x}$:
$\frac{10}{3x} \times \frac{2x}{5}$

Step2: Simplify the expression

Cancel common factors $5$ and $x$, then compute $\frac{10 \times 2}{3 \times 5}$:
$\frac{2 \times 2}{3} = \frac{4}{3}$

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Step1: Rewrite division as multiplication

For $\frac{c}{8} \div \frac{cd}{5}$:
$\frac{c}{8} \times \frac{5}{cd}$

Step2: Simplify the expression

Cancel common factor $c$, then combine terms:
$\frac{5}{8d}$

Answer:

1. $6$
2. $\frac{4}{3}$
3. $\frac{5}{8d}$