How do you evaluate \frac{-14}{13}\div \frac{1}{14}?

Jun 28, 2017

$- \frac{196}{13}$

Explanation:

1. We can turn this division process into a multiplication process by flipping the numerator and denominator of the second fraction. Change the division symbol to a multiplication symbol.

$- \frac{14}{13} \div \frac{\textcolor{red}{1}}{\textcolor{b l u e}{14}}$

$- \frac{14}{13} \times \frac{\textcolor{b l u e}{14}}{\textcolor{red}{1}}$.

An easier way of visualizing this rule is using the expression $1 \div 2$.

$2$ is really $\frac{2}{1}$, so if we flip the numerator and denominator, we can rewrite the expression as $1 \times \frac{1}{2}$.

Dividing by $2$ and multiplying by $\frac{1}{2}$ yield the same result; they are just different ways to represent the same process.

2. Now that we have a multiplication process, the fractions are much easier to combine.

Multiply the numerator of the first fraction by the numerator of the second fraction. Multiply the denominator of the first fraction by the denominator of the second fraction.

Numerators: $- 14 \times 14 = - 196$
Denominators: $13 \times 1 = 13$

$- \frac{14}{13} \times \frac{14}{1}$

$- \frac{196}{13}$

This fraction cannot be simplified any further, so that's your final answer!