Chapter 0.4, Problem 38E

To determine

To calculate: The simplified form of $-\frac{4}{5}+\left(-\frac{1}{3}\right)$ .

Answer to Problem 38E

The simplified form of $-\frac{4}{5}+\left(-\frac{1}{3}\right)$ is $-\frac{17}{15}$ .

Explanation of Solution

Given information:

The statement “ $-\frac{4}{5}+\left(-\frac{1}{3}\right)$ .”

Formula used:

When two fractions with different denominators are subtracted then the two unlike fractions are converted into like fractions by multiplying the denominators with a common factor of their lowest common multiple(LCM).

Consider the provided statement “ $-\frac{4}{5}+\left(-\frac{1}{3}\right)$ .”

Recall that when two fractions with different denominators are subtracted then the two unlike fractions are converted into like fractions by multiplying the denominators with a common factor of their lowest common multiple(LCM).

LCM of $5$ and $3$ is $15$ .

So, multiply $\frac{4}{5}$ by 3 and $\frac{1}{3}$ by 5 in both numerator and denominator,

Thus, the given expression can be simplified as,

  $\begin{array}{c}-\frac{4}{5}+\left(-\frac{1}{3}\right)=-\frac{4\times 3}{5\times 3}+\left(-\frac{1\times 5}{3\times 5}\right)\\ -\frac{4}{5}+\left(-\frac{1}{3}\right)=-\frac{12}{15}+\left(-\frac{5}{15}\right)\\ -\frac{4}{5}+\left(-\frac{1}{3}\right)=-\frac{12}{15}-\frac{5}{15}\\ -\frac{4}{5}+\left(-\frac{1}{3}\right)=-\frac{17}{15}\end{array}$

Since, $-\frac{17}{15}$ cannot be simplified further,

Hence, the simplified form of $-\frac{4}{5}+\left(-\frac{1}{3}\right)$ is $-\frac{17}{15}$ .