Simplify 1/5-3/(4w)+3/(10w)

$\frac{1}{5} - \frac{3}{4 w} + \frac{3}{10 w}$

Step 1

Find the common denominator.

Multiply $\frac{1}{5}$ by $\frac{4 w}{4 w}$ .

$\frac{1}{5} \cdot \frac{4 w}{4 w} - \frac{3}{4 w} + \frac{3}{10 w}$

Multiply $\frac{1}{5}$ by $\frac{4 w}{4 w}$ .

$\frac{4 w}{5 (4 w)} - \frac{3}{4 w} + \frac{3}{10 w}$

Multiply $\frac{3}{4 w}$ by $\frac{5}{5}$ .

$\frac{4 w}{5 (4 w)} - (\frac{3}{4 w} \cdot \frac{5}{5}) + \frac{3}{10 w}$

Multiply $\frac{3}{4 w}$ by $\frac{5}{5}$ .

$\frac{4 w}{5 (4 w)} - \frac{3 \cdot 5}{4 w \cdot 5} + \frac{3}{10 w}$

Multiply $\frac{3}{10 w}$ by $\frac{2}{2}$ .

$\frac{4 w}{5 (4 w)} - \frac{3 \cdot 5}{4 w \cdot 5} + \frac{3}{10 w} \cdot \frac{2}{2}$

Multiply $\frac{3}{10 w}$ by $\frac{2}{2}$ .

$\frac{4 w}{5 (4 w)} - \frac{3 \cdot 5}{4 w \cdot 5} + \frac{3 \cdot 2}{10 w \cdot 2}$

Reorder the factors of $5 (4 w)$ .

$\frac{4 w}{4 \cdot 5 w} - \frac{3 \cdot 5}{4 w \cdot 5} + \frac{3 \cdot 2}{10 w \cdot 2}$

Multiply $4$ by $5$ .

$\frac{4 w}{20 w} - \frac{3 \cdot 5}{4 w \cdot 5} + \frac{3 \cdot 2}{10 w \cdot 2}$

Reorder the factors of $4 w \cdot 5$ .

$\frac{4 w}{20 w} - \frac{3 \cdot 5}{4 \cdot 5 w} + \frac{3 \cdot 2}{10 w \cdot 2}$

Multiply $4$ by $5$ .

$\frac{4 w}{20 w} - \frac{3 \cdot 5}{20 w} + \frac{3 \cdot 2}{10 w \cdot 2}$

Reorder the factors of $10 w \cdot 2$ .

$\frac{4 w}{20 w} - \frac{3 \cdot 5}{20 w} + \frac{3 \cdot 2}{2 \cdot 10 w}$

Multiply $2$ by $10$ .

$\frac{4 w}{20 w} - \frac{3 \cdot 5}{20 w} + \frac{3 \cdot 2}{20 w}$

Step 2

Combine the numerators over the common denominator.

$\frac{4 w - 3 \cdot 5 + 3 \cdot 2}{20 w}$

Step 3

Simplify each term.

Multiply $- 3$ by $5$ .

$\frac{4 w - 15 + 3 \cdot 2}{20 w}$

Multiply $3$ by $2$ .

$\frac{4 w - 15 + 6}{20 w}$

Step 4

Add $- 15$ and $6$ .

$\frac{4 w - 9}{20 w}$