Question

Evaluate the expression. Write fraction in simplest form.

$\frac{{\displaystyle \frac{14}{9}}}{{\displaystyle \frac{1}{3}}-{\displaystyle \frac{1}{6}}}$

Answer 1

Step 1: Simplify the expression given in denominator of given expression

We have given $\frac{{\displaystyle \frac{14}{9}}}{{\displaystyle \frac{1}{3}}-{\displaystyle \frac{1}{6}}}$

The expression in denominator is $\frac{1}{3}-\frac{1}{6}$

$\begin{array}{rcl}\frac{1}{3}-\frac{1}{6}& =& \frac{1\times 2}{3\times 2}-\frac{1}{6}\\ & =& \frac{2}{6}-\frac{1}{6}\\ & =& \frac{1}{6}\end{array}$

$\Rightarrow \frac{{\displaystyle \frac{14}{9}}}{{\displaystyle \frac{1}{3}}-{\displaystyle \frac{1}{6}}}=\frac{{\displaystyle \frac{14}{9}}}{{\displaystyle \frac{1}{6}}}$

Step 2: Simplify the fraction obtained in step 1

Now, $\frac{{\displaystyle \frac{14}{9}}}{{\displaystyle \frac{1}{6}}}=\frac{14\times 6}{1\times 9}$ (since $\frac{{\displaystyle \frac{a}{b}}}{{\displaystyle \frac{c}{d}}}=\frac{a}{b}\times \frac{d}{c}$)

$\Rightarrow \frac{{\displaystyle \frac{14}{9}}}{{\displaystyle \frac{1}{6}}}=\frac{28}{3}$

$\Rightarrow \frac{{\displaystyle \frac{14}{9}}}{{\displaystyle \frac{1}{3}}-{\displaystyle \frac{1}{6}}}=\frac{{\displaystyle 28}}{{\displaystyle 3}}$

Hence, The value of given expression in simplest form is $\frac{28}{3}$.