Q35. - Algebra 1

Question

Find each product or quotient. Write in the simplest form.

$\frac{7}{18}÷\left(-\frac{14}{15}\right)$

Step-by-Step Solution

Answer

The quotient is $-\frac{5}{12}$.

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

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 get the quotient of fractions, multiply dividend to the reciprocal of the divisor and then simplify.

Step 3. Evaluate the quotient.

$\begin{array}{l}=\frac{7}{18}÷\left(-\frac{14}{15}\right)\\ =-\frac{7}{18}\times \frac{15}{14}\\ =-\frac{7\times 3\times 5}{2\times 3\times 3\times 7\times 2}\\ =-\frac{5}{12}\end{array}$

Therefore, the quotient is $-\frac{5}{12}$.