Q37. - Algebra 1

Question

Find the following quotient.

$2\frac{1}{4}÷\frac{1}{2}$

Step-by-Step Solution

Answer

The quotient is $\frac{9}{2}$.

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 $\frac{1}{2}$

$\frac{1}{2}·2=1$

Hence the reciprocal of $\frac{1}{2}$ is  2.

Step 4. Find the quotient of the given numbers.

First, convert mixed fraction into an improper fraction and then calculate the quotient of two fractions:

$2\frac{1}{4}=\frac{2\times 4+1}{4}=\frac{9}{4}$

So, the quotient becomes

$$\begin{gathered} 2\frac{1}{4}÷\frac{1}{2}=\frac{9}{4}÷\frac{1}{2} \\ =\frac{9}{4}\times \frac{2}{1} \\ =\frac{9}{2} \end{gathered}$$