Evaluate 1/3-2/5*1/2

$\frac{1}{3} - \frac{2}{5} \cdot \frac{1}{2}$

Step 1

Simplify each term.

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{2}{5}$ into the numerator.

$\frac{1}{3} + \frac{- 2}{5} \cdot \frac{1}{2}$

Factor $2$ out of $- 2$ .

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

Cancel the common factor.

$\frac{1}{3} + \frac{2 \cdot - 1}{5} \cdot \frac{1}{2}$

Rewrite the expression.

$\frac{1}{3} + \frac{- 1}{5}$

Move the negative in front of the fraction.

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

Step 2

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

Step 3

To write $- \frac{1}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 4

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{3}$ by $\frac{5}{5}$ .

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

Multiply $3$ by $5$ .

$\frac{5}{15} - \frac{1}{5} \cdot \frac{3}{3}$

Multiply $\frac{1}{5}$ by $\frac{3}{3}$ .

$\frac{5}{15} - \frac{3}{5 \cdot 3}$

Multiply $5$ by $3$ .

$\frac{5}{15} - \frac{3}{15}$

Step 5

Combine the numerators over the common denominator.

$\frac{5 - 3}{15}$

Step 6

Subtract $3$ from $5$ .

$\frac{2}{15}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{2}{15}$

Decimal Form:

$0.1\overline{3}$