Q42. - Algebra 1

Question

Find the following quotient.

$\frac{3}{25}÷\frac{2}{15}$

Step-by-Step Solution

Answer

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

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 

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