Chapter 0.4, Problem 38E

To determine

To find: The simplest form of the given sum or difference.

Answer to Problem 38E

The simplest form of the difference is $-\frac{17}{15}$ .

Explanation of Solution

Given:

The given difference is $-\frac{4}{5}+\left(-\frac{1}{3}\right)$ .

Calculation:

Consider the given difference,

  $-\frac{4}{5}+\left(-\frac{1}{3}\right)$

Consider the factors of 3 is,

  $3=3\times 1$

Consider the factors of 5 is,

  $5=5\times 1$

Consider the LCM of 3 and 5 is,

  $3\times 5=15$

Consider the fraction $\frac{4}{5}$ as,

  $\begin{array}{c}\frac{4}{5}=\frac{4\times 3}{5\times 3}\\ =\frac{12}{15}\end{array}$

Consider the fraction $\frac{1}{3}$ as,

  $\begin{array}{c}\frac{1}{3}=\frac{1\times 5}{3\times 5}\\ =\frac{5}{15}\end{array}$

Then, the difference is,

  $-\frac{12}{15}+\left(\frac{-5}{15}\right)$

The product of a negative and positive is a positive then,

  $\begin{array}{c}-\frac{12}{15}+\left(\frac{-5}{15}\right)=-\frac{12}{15}-\frac{5}{15}\\ =\frac{-12-5}{15}\\ =-\frac{17}{15}\end{array}$