Question

Add$\frac{1}{2m}+\frac{7}{8m^{2}n}$.

Short answer

The sum is$\frac{4mn+7}{8m^{2}n}$.

Step-by-step solution

Given Information

The Given expression is$\frac{1}{2m}+\frac{7}{8m^{2}n}$.

Find the LCD of denominators.

Factor the denominators.

$2m=2·m$

$8m^{2}n=2·2·2·m·m·n$

LCD$=2·2·2·m·m·n$

LCD$=8m^{2}n$

Rewrite each fraction as an equivalent fraction with the LCD.

$=\frac{1·4mn}{2m·4mn}+\frac{7·1}{8m^{2}n·1}$

$=\frac{4mn}{8m^{2}n}+\frac{7}{8m^{2}n}$

Add

Take common denominator.

$=\frac{4mn+7}{8m^{2}n}$