Simplify 1/2x-2/5x

$\frac{1}{2} x - \frac{2}{5} x$

Simplify each term.

Combine $\frac{1}{2}$ and $x$ .

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

Combine $x$ and $\frac{2}{5}$ .

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

Move $2$ to the left of $x$ .

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

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

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

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

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

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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

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

Multiply $2$ by $5$ .

$\frac{x \cdot 5}{10} - \frac{2 x}{5} \cdot \frac{2}{2}$

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

$\frac{x \cdot 5}{10} - \frac{2 x \cdot 2}{5 \cdot 2}$

Multiply $5$ by $2$ .

$\frac{x \cdot 5}{10} - \frac{2 x \cdot 2}{10}$

Combine the numerators over the common denominator.

$\frac{x \cdot 5 - 2 x \cdot 2}{10}$

Simplify the numerator.

Factor $x$ out of $x \cdot 5 - 2 x \cdot 2$ .

Factor $x$ out of $x \cdot 5$ .

$\frac{x (5) - 2 x \cdot 2}{10}$

Factor $x$ out of $- 2 x \cdot 2$ .

$\frac{x (5) + x (- 2 \cdot 2)}{10}$

Factor $x$ out of $x (5) + x (- 2 \cdot 2)$ .

$\frac{x (5 - 2 \cdot 2)}{10}$

Multiply $- 2$ by $2$ .

$\frac{x (5 - 4)}{10}$

Subtract $4$ from $5$ .

$\frac{x \cdot 1}{10}$

Multiply $x$ by $1$ .

$\frac{x}{10}$