Chapter 5.5, Problem 9WE

To determine

To simplify the given expression.

Answer to Problem 9WE

  $\frac{r}{3}$

Explanation of Solution

Given:

Expression: $\frac{4r{s}^2}{45}÷\frac{8s}{27r}÷\frac{9rs}{10}$

Concept used:

To divide two fractions, simply flip the second fraction into a reciprocal and change the division sign to a multiplication sign and then multiply the two fractions by multiplying the numerators by each other and denominators by each other. As illustrated below:

  $\frac{a}{b}÷\frac{c}{d}\to \frac{a}{b}\times \frac{d}{c}\to \frac{a\times d}{b\times c}$

Calculation:

Consider the given expression $\frac{4r{s}^2}{45}÷\frac{8s}{27r}÷\frac{9rs}{10}$ ,

  $\frac{4r{s}^2}{45}÷\frac{8s}{27r}÷\frac{9rs}{10}$

  $=\frac{4r{s}^2}{45}\times \frac{27r}{8s}\times \frac{10}{9rs}$  [Flipping second and third fractions]

  $=\frac{4\cancel{r}{\cancel{s}}^{\cancel{2}}}{45}\times \frac{27r}{8\cancel{s}}\times \frac{10}{9\cancel{r}\cancel{s}}$  [Reducing the fractions]

  $=\frac{4}{45}\times \frac{27r}{8}\times \frac{10}{9}$

  $=\frac{1}{9}\times \frac{3r}{2}\times \frac{2}{1}$  [Reducing the fractions]

  $=\frac{1}{3}\times \frac{r}{1}\times \frac{1}{1}$  [Reducing the fractions]

  $\begin{array}{l}=\frac{1\times r\times 1}{3\times 1\times 1}\\ =\frac{r}{3}\end{array}$

Conclusion:

Therefore, after simplification, the answer is $\frac{r}{3}$ .