Algebra Examples

$\frac{11}{9} - \frac{7}{2 w} - \frac{6}{5 w}$

Step 1

Find the common denominator.

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Step 1.1

Multiply $\frac{11}{9}$ by $\frac{10 w}{10 w}$ .

$\frac{11}{9} \cdot \frac{10 w}{10 w} - \frac{7}{2 w} - \frac{6}{5 w}$

Step 1.2

Multiply $\frac{11}{9}$ by $\frac{10 w}{10 w}$ .

$\frac{11 (10 w)}{9 (10 w)} - \frac{7}{2 w} - \frac{6}{5 w}$

Step 1.3

Multiply $\frac{7}{2 w}$ by $\frac{45}{45}$ .

$\frac{11 (10 w)}{9 (10 w)} - (\frac{7}{2 w} \cdot \frac{45}{45}) - \frac{6}{5 w}$

Step 1.4

Multiply $\frac{7}{2 w}$ by $\frac{45}{45}$ .

$\frac{11 (10 w)}{9 (10 w)} - \frac{7 \cdot 45}{2 w \cdot 45} - \frac{6}{5 w}$

Step 1.5

Multiply $\frac{6}{5 w}$ by $\frac{18}{18}$ .

$\frac{11 (10 w)}{9 (10 w)} - \frac{7 \cdot 45}{2 w \cdot 45} - (\frac{6}{5 w} \cdot \frac{18}{18})$

Step 1.6

Multiply $\frac{6}{5 w}$ by $\frac{18}{18}$ .

$\frac{11 (10 w)}{9 (10 w)} - \frac{7 \cdot 45}{2 w \cdot 45} - \frac{6 \cdot 18}{5 w \cdot 18}$

Step 1.7

Reorder the factors of $9 (10 w)$ .

$\frac{11 (10 w)}{9 \cdot 10 w} - \frac{7 \cdot 45}{2 w \cdot 45} - \frac{6 \cdot 18}{5 w \cdot 18}$

Step 1.8

Multiply $9$ by $10$ .

$\frac{11 (10 w)}{90 w} - \frac{7 \cdot 45}{2 w \cdot 45} - \frac{6 \cdot 18}{5 w \cdot 18}$

Step 1.9

Reorder the factors of $2 w \cdot 45$ .

$\frac{11 (10 w)}{90 w} - \frac{7 \cdot 45}{2 \cdot 45 w} - \frac{6 \cdot 18}{5 w \cdot 18}$

Step 1.10

Multiply $2$ by $45$ .

$\frac{11 (10 w)}{90 w} - \frac{7 \cdot 45}{90 w} - \frac{6 \cdot 18}{5 w \cdot 18}$

Step 1.11

Reorder the factors of $5 w \cdot 18$ .

$\frac{11 (10 w)}{90 w} - \frac{7 \cdot 45}{90 w} - \frac{6 \cdot 18}{5 \cdot 18 w}$

Step 1.12

Multiply $5$ by $18$ .

$\frac{11 (10 w)}{90 w} - \frac{7 \cdot 45}{90 w} - \frac{6 \cdot 18}{90 w}$

Step 2

Combine the numerators over the common denominator.

$\frac{11 (10 w) - 7 \cdot 45 - 6 \cdot 18}{90 w}$

Step 3

Simplify each term.

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Step 3.1

Multiply $10$ by $11$ .

$\frac{110 w - 7 \cdot 45 - 6 \cdot 18}{90 w}$

Step 3.2

Multiply $- 7$ by $45$ .

$\frac{110 w - 315 - 6 \cdot 18}{90 w}$

Step 3.3

Multiply $- 6$ by $18$ .

$\frac{110 w - 315 - 108}{90 w}$

Step 4

Subtract $108$ from $- 315$ .

$\frac{110 w - 423}{90 w}$