How do you solve \frac { - 2} { 3} \div 1\frac { 4} { 5}?

Jan 30, 2018

$- \frac{10}{27}$

Explanation:

First, we write them as fractions.
$- \frac{2}{3} \div \frac{4 + \textcolor{red}{5} \cdot 1}{5} = - \frac{2}{3} \div \frac{9}{5}$
If we divide fractions, we swap the denominator and the counter.
$- \frac{2}{3} \div \frac{9}{5} = - \frac{2}{3} \cdot \frac{5}{9} = - \frac{2 \cdot 5}{3 \cdot 9} = - \frac{10}{27}$

Jan 30, 2018

See a solution process below:

Explanation:

First, convert the mixed number to an improper fraction:

$1 \frac{4}{5} = 1 + \frac{4}{5} = \left(\frac{5}{5} \times 1\right) + \frac{4}{5} = \frac{5}{5} + \frac{4}{5} = \frac{5 + 4}{5} = \frac{9}{5}$

Next rewrite the expression as:

$\frac{- 2}{3} \div \frac{9}{5} \implies \frac{\frac{- 2}{3}}{\frac{9}{5}}$

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

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

$\frac{\frac{\textcolor{red}{\left(- 2\right)}}{\textcolor{b l u e}{3}}}{\frac{\textcolor{g r e e n}{9}}{\textcolor{p u r p \le}{5}}} \implies \frac{\textcolor{red}{\left(- 2\right)} \times \textcolor{p u r p \le}{5}}{\textcolor{b l u e}{3} \times \textcolor{g r e e n}{9}} \implies \frac{- 10}{27} \implies - \frac{10}{27}$

Jan 30, 2018

Ok , so it is simple fraction division, but the mixed number must be changed to improper fraction.

Explanation:

You first change the mixed fraction to an improper fraction, which is $\frac{9}{5}$

Then reciprocate(flip over) The $\frac{9}{5}$ to make it $\frac{5}{9}$.

The final equation before the main calculation must look like this:

$\frac{- 2}{3} \cdot \frac{5}{9}$
multiply. The -2 multiplying the 5 and the 3 multiplying the 9.

= $- \frac{10}{27}$