Chapter 0.4, Problem 25E

To determine

To calculate: The simplified form of $\frac{13}{20}-\frac{2}{5}$ .

Answer to Problem 25E

The simplified form of $\frac{13}{20}-\frac{2}{5}$ is $\frac{1}{4}$ .

Explanation of Solution

Given information:

The statement “ $\frac{13}{20}-\frac{2}{5}$ .”

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 “ $\frac{13}{20}-\frac{2}{5}$ .”

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).

LCM of $20$ and $5$ is $20$ .

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

Thus, the given expression can be simplified as,

  $\begin{array}{c}\frac{13}{20}-\frac{2}{5}=\frac{13}{20}-\frac{2\times 4}{5\times 4}\\ \frac{13}{20}-\frac{2}{5}=\frac{13}{20}-\frac{8}{20}\\ \frac{13}{20}-\frac{2}{5}=\frac{13-8}{20}\\ \frac{13}{20}-\frac{2}{5}=\frac{5}{20}\end{array}$

Now,

5 can be expressed as the product of 5 and 1.

20 can be expressed as the product of 5 and 4.

So, $\frac{5}{20}$ can be simplified as,

  $\frac{5}{20}=\frac{5\times 1}{5\times 4}$

Striking off the common terms, we get,

  $\frac{5}{20}=\frac{1}{4}$

Hence, the simplified form of $\frac{13}{20}-\frac{2}{5}$ is $\frac{1}{4}$ .