Q21. - Algebra 1

Question

The simplified form of $\frac{1}{2}-\frac{1}{3}$.

Step-by-Step Solution

Answer

The simplified form of $\frac{1}{2}-\frac{1}{3}$ is $\frac{1}{6}$.

Step 1.

The statement “$\frac{1}{2}-\frac{1}{3}$.”

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 “$\frac{1}{2}-\frac{1}{3}$.”

 

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 3 is 6.

 

So, multiply $\frac{1}{2}$ by 3 and $\frac{1}{3}$ by 2 in both numerator and denominator,

 

Thus, the given expression can be simplified as,

$\frac{1}{2}-\frac{1}{3}=\frac{1\times 3}{2\times 3}-\frac{1\times 2}{3\times 2}$

$\frac{1}{2}-\frac{1}{3}=\frac{3}{6}-\frac{2}{6}$

$\frac{1}{2}-\frac{1}{3}=\frac{3-2}{6}$

$\frac{1}{2}-\frac{1}{3}=\frac{1}{6}$

Step 4. Recheck.

Since, $\frac{1}{6}$ cannot be simplified further,

 

Hence, the simplified form of $\frac{1}{2}-\frac{1}{3}$ is $\frac{1}{6}$.