Question

Find the following quotient.

$\frac{3}{25}÷\frac{2}{15}$

Short answer

The product is $\frac{9}{10}$.

Step-by-step solution

Step 1. Formula Used.

The division of two fractions is given by multiplying the first fraction by the reciprocal of the second fraction.

$\frac{a}{b}÷\frac{c}{d}=\frac{a}{b}\times \frac{d}{c}$

Step 2. Definition of reciprocal.

The product of any number and its reciprocal is 1.

Step 3. Find the reciprocal of the given number.

Reciprocal of$\frac{2}{15}$

$\frac{2}{15}·\frac{15}{2}=1$

Hence, reciprocal of $\frac{2}{15}$is $\frac{15}{2}$.

Step 4. Find the quotient of the given numbers.

By using the formula of the division of two fractions

$$\begin{gathered} \frac{3}{25}÷\frac{2}{15}=\frac{3}{25}\times \frac{15}{2} \\ =\frac{3\times 15}{25\times 2} \\ =\frac{45}{50} \\ =\frac{5\times 9}{5\times 10} \left[\mathrm{divide}N\&D\mathrm{by}\mathrm{common}\mathrm{factor}5\right] \\ =\frac{\frac{5}{5}\times 9}{\frac{5}{5}\times 10} \\ =\frac{1\times 9}{1\times 10} \\ =\frac{9}{10} \end{gathered}$$