Q22. - Algebra 1

Question

The simplified form of $\frac{3}{7}+\frac{5}{14}$.

Step-by-Step Solution

Answer

The simplified form of $\frac{3}{7}+\frac{5}{14}$ is $\frac{11}{14}$.

Step 1. Given

The statement “$\frac{3}{7}+\frac{5}{14}$.”

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 “$\frac{3}{7}+\frac{5}{14}$.”

 

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 7 and 14 is 14.

 

So, multiply $\frac{3}{7}$ by 2 in both numerator and denominator,

 

Thus, the given expression can be simplified as,

$\frac{3}{7}+\frac{5}{14}=\frac{3\times 2}{7\times 2}+\frac{5}{14}$

$\frac{3}{7}+\frac{5}{14}=\frac{6}{14}+\frac{5}{14}$

$\frac{3}{7}+\frac{5}{14}=\frac{6+5}{14}$

$\frac{3}{7}+\frac{5}{14}=\frac{11}{14}$

Step 4. Recheck.

Since, $\frac{11}{14}$ cannot be simplified further,

Hence, the simplified form of $\frac{3}{7}+\frac{5}{14}$ is $\frac{11}{14}$.