How do you simplify \frac { 2} { 3} \div 1\frac { 3} { 5}?

1 Answer
Mar 4, 2018

See a solution process below:

Explanation:

First, we can rewrite the mixed number as an improper fraction:

$1 \frac{3}{5} = 1 + \frac{3}{5} = \left(\frac{5}{5} \times 1\right) + \frac{3}{5} = \frac{5}{5} + \frac{3}{5} = \frac{5 + 3}{5} = \frac{8}{5}$

Next, we can rewrite the expression as;

$\frac{\frac{2}{3}}{\frac{8}{5}}$

We can now use this rule for dividing fractions to evaluate the expression:

$\frac{\frac{\textcolor{red}{a}}{\textcolor{b l u e}{b}}}{\frac{\textcolor{g r e e n}{c}}{\textcolor{p u r p \le}{d}}} = \frac{\textcolor{red}{a} \times \textcolor{p u r p \le}{d}}{\textcolor{b l u e}{b} \times \textcolor{g r e e n}{c}}$

$\frac{\frac{\textcolor{red}{2}}{\textcolor{b l u e}{3}}}{\frac{\textcolor{g r e e n}{8}}{\textcolor{p u r p \le}{5}}} = \frac{\textcolor{red}{2} \times \textcolor{p u r p \le}{5}}{\textcolor{b l u e}{3} \times \textcolor{g r e e n}{8}} = \frac{\cancel{\textcolor{red}{2}} \times \textcolor{p u r p \le}{5}}{\textcolor{b l u e}{3} \times \cancel{\textcolor{g r e e n}{8}} \textcolor{g r e e n}{4}} = \frac{5}{12}$