Question

Find each product or quotient.

$-\frac{2}{21}÷\left(-\frac{2}{15}\right)$

Short answer

The quotient is $\frac{5}{7}$.

Step-by-step solution

Step 1. Concept of the quotient of like and unlike sign integers.

The quotient of two fractions with the same sign is always positive.

The quotient of two fractions with opposite signs is always negative.

Step 2. Concept of the division of fractions.

To divide two fractions, just multiply the reciprocal of the second fraction with the first fraction.

Step 3. Evaluate the quotient.

To find the quotient of the given fractions, find the reciprocal of the second fraction multiply that with the first fraction and simplify further as shown below:

$$\begin{gathered} -\frac{2}{21}÷\left(-\frac{2}{15}\right)=-\frac{2}{21}\times \left(-\frac{15}{2}\right) \\ =\frac{30}{42} \\ =\frac{5}{7} \end{gathered}$$

Therefore, the quotient is $\frac{5}{7}$.