Q24. - Algebra 1

Question

The simplified form of $\frac{3}{8}+\frac{1}{6}$.

Step-by-Step Solution

Answer

The simplified form of $\frac{3}{8}+\frac{1}{6}$ is $\frac{13}{24}$.

Step 1.

The statement “$\frac{3}{8}+\frac{1}{6}$.”

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 “$\frac{3}{8}+\frac{1}{6}$.”

 

Recall that when two fractions with different denominators are added 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 8 and 6 is 12.

 

So, multiply $\frac{3}{8}$ by 3 and $\frac{1}{6}$ by 4 in both numerator and denominator,

 

Thus, the given expression can be simplified as,

$\frac{3}{8}+\frac{1}{6}=\frac{3\times 3}{8\times 3}+\frac{1\times 4}{6\times 4}$

$\frac{3}{8}+\frac{1}{6}=\frac{9}{24}+\frac{4}{24}$

$\frac{3}{8}+\frac{1}{6}=\frac{9+4}{24}$

$\frac{3}{8}+\frac{1}{6}=\frac{13}{24}$

Step 4. Recheck.

Since, $\frac{13}{24}$ cannot be simplified further,

 

Hence, the simplified form of $\frac{3}{8}+\frac{1}{6}$ is $\frac{13}{24}$.