How do you divide 1 2/3 by 2 3/4?

Dec 7, 2016

$\frac{20}{33}$

Explanation:

First, we need to convert each mixed fraction to an improper fraction

$1 \frac{2}{3} = \left(\frac{3}{3} \times 1\right) + \frac{2}{3} \to \frac{3}{3} + \frac{2}{3} \to \frac{5}{3}$

$2 \frac{3}{4} \to \left(\frac{4}{4} \times 2\right) + \frac{3}{4} \to \frac{8}{4} + \frac{3}{4} \to \frac{11}{4}$

Now we can write the division problem as

$\frac{\frac{5}{3}}{\frac{11}{4}}$

The rule for dividing fractions is:

$\textcolor{red}{\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a \cdot d}{b \cdot c}}$

We can use this rule to divide and solve our problem:

$\frac{5 \cdot 4}{3 \cdot 11}$

$\frac{20}{33}$