# How do you evaluate \frac{5}{-8}\div 1\frac{3}{7}?

Nov 13, 2017

See a solution process below:

#### Explanation:

First, rewrite the mixed number as an improper fraction:

$1 \frac{3}{7} = 1 + \frac{3}{7} = \left(\frac{7}{7} \times 1\right) + \frac{3}{7} = \frac{7}{7} + \frac{3}{7} = \frac{7 + 3}{7} = \frac{10}{7}$

Next, we can rewrite the expression as:

$\frac{5}{-} 8 \div 1 \frac{3}{7} \implies \frac{5}{-} 8 \div \frac{10}{7} \implies \frac{\frac{5}{-} 8}{\frac{10}{7}}$

Now, use this rule for dividing fractions to evaluate the expression:

$\frac{\frac{\textcolor{red}{5}}{\textcolor{b l u e}{- 8}}}{\frac{\textcolor{g r e e n}{10}}{\textcolor{p u r p \le}{7}}} \implies$

$\frac{\textcolor{red}{5} \times \textcolor{p u r p \le}{7}}{\textcolor{b l u e}{- 8} \times \textcolor{g r e e n}{10}} \implies$

$\frac{\textcolor{red}{5} \times \textcolor{p u r p \le}{7}}{\textcolor{b l u e}{- 8} \times \textcolor{g r e e n}{5 \times 2}} \implies$

$\frac{\cancel{\textcolor{red}{5}} \times \textcolor{p u r p \le}{7}}{\textcolor{b l u e}{- 8} \times \cancel{\textcolor{g r e e n}{5}} \times \textcolor{g r e e n}{2}} \implies$

$\frac{7}{-} 16 \implies$

$- \frac{7}{16}$