Simplify (2x)/3+1/2

$\frac{2 x}{3} + \frac{1}{2}$

Step 1

To write $\frac{2 x}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{2 x}{3} \cdot \frac{2}{2} + \frac{1}{2}$

Step 2

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{2 x}{3} \cdot \frac{2}{2} + \frac{1}{2} \cdot \frac{3}{3}$

Step 3

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{2 x}{3}$ by $\frac{2}{2}$ .

$\frac{2 x \cdot 2}{3 \cdot 2} + \frac{1}{2} \cdot \frac{3}{3}$

Multiply $3$ by $2$ .

$\frac{2 x \cdot 2}{6} + \frac{1}{2} \cdot \frac{3}{3}$

Multiply $\frac{1}{2}$ by $\frac{3}{3}$ .

$\frac{2 x \cdot 2}{6} + \frac{3}{2 \cdot 3}$

Multiply $2$ by $3$ .

$\frac{2 x \cdot 2}{6} + \frac{3}{6}$

Step 4

Combine the numerators over the common denominator.

$\frac{2 x \cdot 2 + 3}{6}$

Step 5

Multiply $2$ by $2$ .

$\frac{4 x + 3}{6}$