Simplify (5m)/(2n)+(3m)/(4n)

$\frac{5 m}{2 n} + \frac{3 m}{4 n}$

To write $\frac{5 m}{2 n}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{5 m}{2 n} \cdot \frac{2}{2} + \frac{3 m}{4 n}$

Write each expression with a common denominator of $4 n$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{5 m}{2 n}$ by $\frac{2}{2}$ .

$\frac{5 m \cdot 2}{2 n \cdot 2} + \frac{3 m}{4 n}$

Multiply $2$ by $2$ .

$\frac{5 m \cdot 2}{4 n} + \frac{3 m}{4 n}$

Combine the numerators over the common denominator.

$\frac{5 m \cdot 2 + 3 m}{4 n}$

Simplify the numerator.

Factor $m$ out of $5 m \cdot 2 + 3 m$ .

Factor $m$ out of $5 m \cdot 2$ .

$\frac{m (5 \cdot 2) + 3 m}{4 n}$

Factor $m$ out of $3 m$ .

$\frac{m (5 \cdot 2) + m \cdot 3}{4 n}$

Factor $m$ out of $m (5 \cdot 2) + m \cdot 3$ .

$\frac{m (5 \cdot 2 + 3)}{4 n}$

Multiply $5$ by $2$ .

$\frac{m (10 + 3)}{4 n}$

Add $10$ and $3$ .

$\frac{m \cdot 13}{4 n}$

Move $13$ to the left of $m$ .

$\frac{13 m}{4 n}$