Q36. - Algebra 1

Question

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

Step-by-Step Solution

Answer

The simplified form of $\frac{1}{2}-\frac{4}{5}$ is $-\frac{3}{10}$.

Step 1. Given

The statement “$\frac{1}{2}-\frac{4}{5}$.”

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 “$\frac{1}{2}-\frac{4}{5}$.”

 

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 2 and 5 is 10.

 

So, multiply $\frac{1}{2}$ by 5 and $\frac{4}{5}$ by 2 in both numerator and denominator,

 

Thus, the given expression can be simplified as,

$\frac{1}{2}-\frac{4}{5}=\frac{1\times 5}{2\times 5}-\frac{4\times 2}{5\times 2}$

$\frac{1}{2}-\frac{4}{5}=\frac{5}{10}-\frac{8}{10}$

$\frac{1}{2}-\frac{4}{5}=\frac{5-8}{10}$

$\frac{1}{2}-\frac{4}{5}=\frac{-3}{10}$

Step 4. Recheck.

Since, $\frac{-3}{10}$ cannot be simplified further,

 

Hence, the simplified form of $\frac{1}{2}-\frac{4}{5}$ is $\frac{-3}{10}$.