Q31. - Algebra 1

Question

Find the following quotient.

$\frac{2}{3}÷\frac{1}{3}$

Step-by-Step Solution

Answer

The quotient is 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 second fraction.

Reciprocal of $\frac{1}{3}$

$\frac{1}{3}·3=1$

Hence, the reciprocal of $\frac{1}{3}$ is 3.

Step 4. Find the quotient of the given numbers.

Now by the definition of the quotient of two fractions:

$\frac{2}{3}÷\frac{1}{3}=\frac{2}{3}\times 3=2$