Evaluate 2/5-2/3

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

Step 1

To write $\frac{2}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 2

To write $- \frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

Step 3

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

Multiply $\frac{2}{5}$ by $\frac{3}{3}$ .

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

Multiply $5$ by $3$ .

$\frac{2 \cdot 3}{15} - \frac{2}{3} \cdot \frac{5}{5}$

Multiply $\frac{2}{3}$ by $\frac{5}{5}$ .

$\frac{2 \cdot 3}{15} - \frac{2 \cdot 5}{3 \cdot 5}$

Multiply $3$ by $5$ .

$\frac{2 \cdot 3}{15} - \frac{2 \cdot 5}{15}$

Step 4

Combine the numerators over the common denominator.

$\frac{2 \cdot 3 - 2 \cdot 5}{15}$

Step 5

Simplify the numerator.

Multiply $2$ by $3$ .

$\frac{6 - 2 \cdot 5}{15}$

Multiply $- 2$ by $5$ .

$\frac{6 - 10}{15}$

Subtract $10$ from $6$ .

$\frac{- 4}{15}$

Step 6

Move the negative in front of the fraction.

$- \frac{4}{15}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{4}{15}$

Decimal Form:

$- 0.2\overline{6}$