# How do you simplify 6/7 div4/5?

Mar 23, 2018

$\frac{6}{7} \div \frac{4}{5} = \frac{15}{14} = 1 \frac{1}{14}$

#### Explanation:

Simplify:

$\frac{6}{7} \div \frac{4}{5}$

When dividing by a fraction, invert the fraction and multiply the numerators and denominators.

$\frac{6}{7} \times \frac{5}{4}$

$\frac{6 \times 5}{7 \times 4}$

Simplify.

$\frac{30}{28}$

We can reduce the fraction by dividing the numerator and denominator by $2$.

$\frac{30 \div 2}{28 \div 2}$

Simplify.

$\frac{15}{14}$

$\frac{15}{14}$ is an improper fraction, which can be converted into a mixed number $\left(\textcolor{red}{a} \frac{\textcolor{b l u e}{b}}{\textcolor{g r e e n}{c}}\right)$ by dividing $15$ by $14$ using long division to get a whole number quotient and a remainder.

$15 \div 14 = \text{1 remainder 1}$

The whole number quotient becomes the whole number of the mixed number, the remainder becomes the numerator, and the divisor $\left(14\right)$ remains the denominator.

15/14=color(red)(1) color(blue)(1)/color(green)(14