Chapter 6.2, Problem 5WE

To determine

To calculate: The simplified form of the expression $\frac{3}{5}\cdot \frac{5}{7}\cdot \frac{7}{9}$.

Answer to Problem 5WE

The simplified form of the expression $\frac{3}{5}\cdot \frac{5}{7}\cdot \frac{7}{9}$ is $\frac{1}{3}$.

Explanation of Solution

Given information:

The expression $\frac{3}{5}\cdot \frac{5}{7}\cdot \frac{7}{9}$.

Formula used:

Fractions are multiplied as $\frac{a}{b}\cdot \frac{c}{d}=\frac{ab}{cd}$.

Calculation:

Consider the expression $\frac{3}{5}\cdot \frac{5}{7}\cdot \frac{7}{9}$.

Recall that fractions are multiplied as $\frac{a}{b}\cdot \frac{c}{d}=\frac{ab}{cd}$.

Apply it,

  $\begin{array}{c}\frac{3}{5}\cdot \frac{5}{7}\cdot \frac{7}{9}=\frac{3\times 5}{5\times 7}\cdot \frac{7}{9}\\ =\frac{3}{7}\cdot \frac{7}{9}\\ =\frac{3\times 7}{7\times 9}\\ =\frac{3}{9}\end{array}$

Simplify it further as,

  $\begin{array}{c}\frac{3}{5}\cdot \frac{5}{7}\cdot \frac{7}{9}=\frac{3}{9}\\ =\frac{1}{3}\end{array}$

Thus, the simplified form of the expression $\frac{3}{5}\cdot \frac{5}{7}\cdot \frac{7}{9}$ is $\frac{1}{3}$.