Problem 116 - Introductory Algebra for College Students

Question

Perform the indicated operation. Write the answer as an algebraic expression. $$\frac{2}{3} \div \frac{a}{7}$$

Step-by-Step Solution

Answer

\(\frac{14}{3a}\)

Step 1: Identify the Reciprocal of the Fraction

The reciprocal of a fraction is obtained by interchanging its numerator and its denominator. Thus, the reciprocal of \(\frac{a}{7}\) is \(\frac{7}{a}\).

Step 2: Replace Division With Multiplication by the Reciprocal

The expression \(\frac{2}{3} \div \frac{a}{7}\) then becomes \(\frac{2}{3} \times \frac{7}{a}\)

Step 3: Multiply

Multiplying the fractions, results in \(\frac{2 \times 7}{3 \times a}\). Which simplifies to \(\frac{14}{3a}\).