Question

find the quotient. write fractions in simplest form.
$-\frac{5}{6} div \frac{3}{10} = \square$

Explanation:

Step1: Recall division of fractions rule

To divide two fractions, we multiply the first fraction by the reciprocal of the second fraction. The reciprocal of $\frac{3}{10}$ is $\frac{10}{3}$. So, $-\frac{5}{6} \div \frac{3}{10}=-\frac{5}{6} \times \frac{10}{3}$.

Step2: Multiply the numerators and denominators

Multiply the numerators: $-5\times10 = -50$. Multiply the denominators: $6\times3 = 18$. So we get $\frac{-50}{18}$.

Step3: Simplify the fraction

We can simplify $\frac{-50}{18}$ by dividing both the numerator and the denominator by their greatest common divisor, which is 2. $\frac{-50\div2}{18\div2}=\frac{-25}{9}$.

Answer:

$-\frac{25}{9}$