Q25. - Algebra 1

Question

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

Step-by-Step Solution

Answer

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

Step 1.

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

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 “$\frac{13}{20}-\frac{2}{5}$.”

 

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,

$\frac{13}{20}-\frac{2}{5}=\frac{13}{20}-\frac{2\times 4}{5\times 4}$

$\frac{13}{20}-\frac{2}{5}=\frac{13}{20}-\frac{8}{20}$

$\frac{13}{20}-\frac{2}{5}=\frac{13-8}{20}$

$\frac{13}{20}-\frac{2}{5}=\frac{5}{20}$

Step 4. Recheck.

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 $\frac{1}{4}$.