Find the Exact Value 2/5(1/3+1/2)

$\frac{2}{5} (\frac{1}{3} + \frac{1}{2})$

Step 1

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

$\frac{2}{5} (\frac{1}{3} \cdot \frac{2}{2} + \frac{1}{2})$

Step 2

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

$\frac{2}{5} (\frac{1}{3} \cdot \frac{2}{2} + \frac{1}{2} \cdot \frac{3}{3})$

Step 3

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

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

$\frac{2}{5} (\frac{2}{3 \cdot 2} + \frac{1}{2} \cdot \frac{3}{3})$

Multiply $3$ by $2$ .

$\frac{2}{5} (\frac{2}{6} + \frac{1}{2} \cdot \frac{3}{3})$

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

$\frac{2}{5} (\frac{2}{6} + \frac{3}{2 \cdot 3})$

Multiply $2$ by $3$ .

$\frac{2}{5} (\frac{2}{6} + \frac{3}{6})$

Step 4

Simplify the expression.

Combine the numerators over the common denominator.

$\frac{2}{5} \cdot \frac{2 + 3}{6}$

Add $2$ and $3$ .

$\frac{2}{5} \cdot \frac{5}{6}$

Step 5

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

$\frac{2}{5} \cdot \frac{5}{2 (3)}$

Cancel the common factor.

$\frac{2}{5} \cdot \frac{5}{2 \cdot 3}$

Rewrite the expression.

$\frac{1}{5} \cdot \frac{5}{3}$

Step 6

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{1}{5} \cdot \frac{5}{3}$

Rewrite the expression.

$\frac{1}{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{3}$

Decimal Form:

$0.\overline{3}$