Question

Evaluate the expression. Write fraction in simplest form.

$\frac{-1{\displaystyle \frac{2}{3}}·\left(-{\displaystyle \frac{3}{5}}\right)}{{\left({\displaystyle \frac{1}{3}}\right)}^2}$

Answer 1

Step 1: Write mixed fraction in simple form

$\frac{-1{\displaystyle \frac{2}{3}}·\left(-{\displaystyle \frac{3}{5}}\right)}{{\left({\displaystyle \frac{1}{3}}\right)}^2}=\frac{-{\displaystyle \frac{5}{3}}·\left(-{\displaystyle \frac{3}{5}}\right)}{{\left({\displaystyle \frac{1}{3}}\right)}^2}$

Step 2: Write ${\left(\frac{1}{3}\right)}^2$ as continued multiplication and use $\frac{a}{b}\times \frac{b}{a}=\frac{1}{1}=1$

$\frac{-{\displaystyle \frac{5}{3}}·\left(-{\displaystyle \frac{3}{5}}\right)}{\left({\displaystyle \frac{1}{3}}\right)\left({\displaystyle \frac{1}{3}}\right)}=\frac{-{\displaystyle \frac{5}{3}}·\left(-{\displaystyle \frac{3}{5}}\right)}{\left({\displaystyle \frac{1}{9}}\right)}=\frac{{\displaystyle \frac{1}{1}}}{{\displaystyle \frac{1}{9}}}$

Step 3: $a÷b=a\times \frac{1}{b}$

$\frac{1}{1}\times \frac{9}{1}=\frac{9}{1}=9$

Hence, the value of expression in simplest form is 9.