Find the Exact Value 1/2+2/3

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

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

Multiply $2$ by $3$ .

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

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

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

Multiply $3$ by $2$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify the numerator.

Multiply $2$ by $2$ .

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

Add $3$ and $4$ .

$\frac{7}{6}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{7}{6}$

Decimal Form:

$1.1\overline{6}$

Mixed Number Form:

$1 \frac{1}{6}$