Chapter 1, Problem 1RE

Express as a simplified rational number:

(a) $\left(\frac{2}{3}\right)\left(-\frac{5}{8}\right)$   (b) $\frac{3}{4}+\frac{6}{5}$   (c) $\frac{5}{8}-\frac{6}{7}$   (d) $\frac{3}{4}÷\frac{6}{5}$

To determine

The simplified form of the rational number.

Answer to Problem 1RE

The simplified form is $\frac{-5}{12}$ .

Explanation of Solution

Given:

  $\left(\frac{2}{3}\right)\left(\frac{-5}{8}\right)$

Formula used:

  $\left(\frac{a}{b}\right)\left(\frac{c}{d}\right)=\left(\frac{a}{b}\right)\times \left(\frac{c}{d}\right)$

  $\begin{array}{l}\left(\frac{2}{3}\right)\left(\frac{-5}{8}\right)\\ \left(\frac{2}{3}\right)\times \left(\frac{-5}{8}\right)\\ \left(\frac{1}{3}\right)\times \left(\frac{-5}{4}\right)\\ \left(\frac{-5}{12}\right)\end{array}$

To determine

The simplified form of the rational number.

Answer to Problem 1RE

The sum of the given rational numbers is $\frac{33}{20}$ .

Explanation of Solution

Given:

  $\frac{3}{4}+\frac{6}{5}$

  $\frac{3}{4}+\frac{6}{5}$

Calculate the LCM of the $4$ and $5$ .

  $\frac{3}{4}+\frac{6}{5}=\frac{15+18}{20}$

The sum of the given rational numbers is $\frac{33}{20}$ .

To determine

The simplified form of the given rational number.

Answer to Problem 1RE

The difference of the given rational numbers is $\frac{-13}{56}$ .

Explanation of Solution

Given:

  $\frac{5}{8}-\frac{6}{7}$

  $\frac{5}{8}-\frac{6}{7}$

Calculate the LCM of the $8$ and $7$ .

  $\frac{5}{8}-\frac{6}{7}=\frac{35-48}{56}$

The difference of the given rational numbers is $\frac{-13}{56}$ .

To determine

The simplified form of the given rational number.

Answer to Problem 1RE

The simplified form is $\left(\frac{5}{8}\right)$ .

Explanation of Solution

Given:

  $\left(\frac{3}{4}\right)÷\left(\frac{6}{5}\right)$

Formula used:

  $\left(\frac{a}{b}\right)÷\left(\frac{c}{d}\right)=\left(\frac{a}{b}\right)\times \left(\frac{d}{c}\right)$

  $\left(\frac{3}{4}\right)÷\left(\frac{6}{5}\right)$

Use formula and multiply the reciprocal of $\left(\frac{6}{5}\right)$ to $\left(\frac{3}{4}\right)$ .

  $\begin{array}{l}\left(\frac{3}{4}\right)\times \left(\frac{5}{6}\right)\\ \left(\frac{1}{4}\right)\times \left(\frac{5}{2}\right)\\ \frac{5}{8}\end{array}$