Chapter 0.4, Problem 35E

To determine

To calculate: The simplified form of $-\frac{1}{6}-\frac{2}{3}$ .

Answer to Problem 35E

The simplified form of $-\frac{1}{6}-\frac{2}{3}$ is $-\frac{5}{6}$ .

Explanation of Solution

Given information:

The statement “ $-\frac{1}{6}-\frac{2}{3}$ .”

Formula used:

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

Consider the provided statement “ $\frac{13}{20}-\frac{2}{5}$ .”

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) and then accordingly adding the two.

LCM of $6$ and $3$ is $6$ .

So, multiply $\frac{2}{3}$ by 2 in both numerator and denominator,

Thus, the given expression can be simplified as,

  $\begin{array}{c}-\frac{1}{6}-\frac{2}{3}=-\frac{1}{6}-\frac{2\times 2}{3\times 2}\\ -\frac{1}{6}-\frac{2}{3}=-\frac{1}{6}-\frac{4}{6}\\ -\frac{1}{6}-\frac{2}{3}=-\left(\frac{1}{6}+\frac{4}{6}\right)\\ -\frac{1}{6}-\frac{2}{3}=-\frac{4+1}{6}\end{array}$

Simplify it further as,

  $-\frac{1}{6}-\frac{2}{3}=-\frac{5}{6}$

Since, it cannot be simplified further,

Hence, the simplified form of $-\frac{1}{6}-\frac{2}{3}$ is $-\frac{5}{6}$ .