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Chapter 1: Problem 116

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

Short Answer

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

Step by step solution

01

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 \(\frac{7}{a}\).
02

Replace Division With Multiplication by the Reciprocal

The expression \(\frac{2}{3} \div \frac{a}{7}\) then becomes \(\frac{2}{3} \times \frac{7}{a}\)
03

Multiply

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

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