Q39. - Algebra 1

Question

Find the following quotient.

$\frac{11}{12}÷1\frac{2}{3}$

Step-by-Step Solution

Answer

The quotient is $\frac{11}{20}$.

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.

First, simplify mixed fraction into improper fraction then find its reciprocal:

$1\frac{2}{3}=\frac{1\times 3+2}{3}=\frac{5}{3}$

Reciprocal of

$\frac{5}{3}·\frac{3}{5}=1$

Hence, the reciprocal of $\frac{2}{3}$ is $\frac{3}{2}$.

Step 4. Find the quotient of the given numbers.

$\begin{array}{c}\frac{11}{12}÷1\frac{2}{3}=\frac{11}{12}÷\frac{5}{3}\\ =\frac{11}{12}\times \frac{3}{5}\\ =\frac{11}{20}\end{array}$