Chapter 4, Problem 25MS

To determine

To simplify the given expression $-2\frac{3}{8}÷\left(-2\frac{1}{8}\right)$ .

Answer to Problem 25MS

  $1\frac{2}{17}$

Explanation of Solution

Given information: $-2\frac{3}{8}÷\left(-2\frac{1}{8}\right)$

Calculations: We have $-2\frac{3}{8}÷\left(-2\frac{1}{8}\right)$

Convert each mixed fraction into improper fraction first:

  $2\frac{3}{8}=\frac{2\times 8+3}{8}=\frac{19}{8}$

  $2\frac{1}{8}=\frac{2\times 8+1}{8}=\frac{17}{8}$

Therefore,

  $-2\frac{3}{8}÷\left(-2\frac{1}{8}\right)\text{ could be written as }-\frac{19}{8}÷\left(-\frac{17}{8}\right)$

Apply rule

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

  $-\frac{19}{8}÷\left(-\frac{17}{8}\right)=-\frac{19}{8}\times \left(-\frac{8}{17}\right)$

Apply rule: $-a\cdot \left(-b\right)=a\cdot b$

  $-\frac{19}{8}\times \left(-\frac{8}{17}\right)=\frac{19}{8}\times \frac{8}{17}$

Cancel common factor 8 in numerators and denominators.

  $\frac{19}{\cancel{8}}\times \frac{\cancel{8}}{17}=\frac{19}{17}$

Now, convert improper fraction in mixed fraction by long division

  $\begin{array}{l}17\begin{array}{c}\hfill 1\\ \hfill \overline{)\begin{array}{l}19\\ -17\end{array}}\end{array}\\ \_\_\_\_\_\_\_\\ \text{ 2 }\end{array}$

  $\Rightarrow \frac{19}{17}=1\frac{2}{17}$

Therefore, $-2\frac{3}{8}÷\left(-2\frac{1}{8}\right)=1\frac{2}{17}$