Q32. - Algebra 1

Question

Find the following quotient.

$\frac{16}{9}÷\frac{4}{9}$

Step-by-Step Solution

Answer

The quotient is 4.

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 $\frac{4}{9}$

$\frac{4}{9}·\frac{9}{4}=1$

Hence, reciprocal of $\frac{4}{9}$ is $\frac{9}{4}$.

Step 4. Find the quotient of the given numbers.

Now by the definition of the quotient of two fractions:

$\begin{array}{c}\frac{16}{9}÷\frac{4}{9}=\frac{16}{9}\times \frac{9}{4}\\ =\frac{16}{4}\\ =4\end{array}$