Chapter 0.4, Problem 37E

To determine

To calculate: The simplified form of $-\frac{2}{5}+\frac{17}{20}$ .

Answer to Problem 37E

The simplified form of $-\frac{2}{5}+\frac{17}{20}$ is $\frac{9}{20}$ .

Explanation of Solution

Given information:

The statement “ $-\frac{2}{5}+\frac{17}{20}$ .”

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 “ $-\frac{2}{5}+\frac{17}{20}$ .”

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 $20$ is $20$ .

So, multiply $\frac{2}{5}$ by 4 in both numerator and denominator,

Thus, the given expression can be simplified as,

  $\begin{array}{c}-\frac{2}{5}+\frac{17}{20}=-\frac{2\times 4}{5\times 4}+\frac{17}{20}\\ -\frac{2}{5}+\frac{17}{20}=-\frac{8}{20}+\frac{17}{20}\\ -\frac{2}{5}+\frac{17}{20}=\frac{-8+17}{20}\\ -\frac{2}{5}+\frac{17}{20}=\frac{9}{20}\end{array}$

Since, $\frac{9}{20}$ cannot be simplified further,

Hence, the simplified form of $-\frac{2}{5}+\frac{17}{20}$ is $\frac{9}{20}$ .