Q37. - Algebra 1

Question

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

Step-by-Step Solution

Answer

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

Step 1.

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

Step 2. Concept.

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).

Step 3. Calculation.

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,

$-\frac{2}{5}+\frac{17}{20}=-\frac{2\times 4}{5\times 4}+\frac{17}{20}$

$-\frac{2}{5}+\frac{17}{20}=-\frac{8}{20}+\frac{17}{20}$

$-\frac{2}{5}+\frac{17}{20}=\frac{-8+17}{20}$

$-\frac{2}{5}+\frac{17}{20}=\frac{9}{20}$

Step 4. Recheck.

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

 

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