Q36. - Algebra 1

Question

Find the following quotient.

$\frac{1}{2}÷\frac{3}{5}$

Step-by-Step Solution

Answer

The quotient is $\frac{5}{6}$.

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 $\frac{3}{5}$

$\frac{3}{5}·\frac{5}{3}=1$

Hence the reciprocal of $\frac{3}{5}$ is $\frac{5}{3}$.

Step 4. Find the quotient of the given numbers.

Now by the definition of the quotient of two fractions:

$\begin{array}{c}\frac{1}{2}÷\frac{3}{5}=\frac{1}{2}\times \frac{5}{3}\\ =\frac{5}{6}\end{array}$