Question

Find the following quotient.

$\frac{3}{2}÷\frac{1}{2}$

Short answer

The quotient is 3.

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$\frac{1}{2}$

$\frac{1}{2}·2=1$

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

Step 4. Find the quotient of the given numbers.

Now by the definition of quotient of two fractions:

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