Trigonometry Examples

$- \frac{2}{3} + \frac{7}{9} - \frac{9}{10}$

Step 1

Find the common denominator.

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Step 1.1

Multiply $\frac{2}{3}$ by $\frac{30}{30}$ .

$- (\frac{2}{3} \cdot \frac{30}{30}) + \frac{7}{9} - \frac{9}{10}$

Step 1.2

Multiply $\frac{2}{3}$ by $\frac{30}{30}$ .

$- \frac{2 \cdot 30}{3 \cdot 30} + \frac{7}{9} - \frac{9}{10}$

Step 1.3

Multiply $\frac{7}{9}$ by $\frac{10}{10}$ .

$- \frac{2 \cdot 30}{3 \cdot 30} + \frac{7}{9} \cdot \frac{10}{10} - \frac{9}{10}$

Step 1.4

Multiply $\frac{7}{9}$ by $\frac{10}{10}$ .

$- \frac{2 \cdot 30}{3 \cdot 30} + \frac{7 \cdot 10}{9 \cdot 10} - \frac{9}{10}$

Step 1.5

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

$- \frac{2 \cdot 30}{3 \cdot 30} + \frac{7 \cdot 10}{9 \cdot 10} - (\frac{9}{10} \cdot \frac{9}{9})$

Step 1.6

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

$- \frac{2 \cdot 30}{3 \cdot 30} + \frac{7 \cdot 10}{9 \cdot 10} - \frac{9 \cdot 9}{10 \cdot 9}$

Step 1.7

Multiply $3$ by $30$ .

$- \frac{2 \cdot 30}{90} + \frac{7 \cdot 10}{9 \cdot 10} - \frac{9 \cdot 9}{10 \cdot 9}$

Step 1.8

Multiply $9$ by $10$ .

$- \frac{2 \cdot 30}{90} + \frac{7 \cdot 10}{90} - \frac{9 \cdot 9}{10 \cdot 9}$

Step 1.9

Reorder the factors of $10 \cdot 9$ .

$- \frac{2 \cdot 30}{90} + \frac{7 \cdot 10}{90} - \frac{9 \cdot 9}{9 \cdot 10}$

Step 1.10

Multiply $9$ by $10$ .

$- \frac{2 \cdot 30}{90} + \frac{7 \cdot 10}{90} - \frac{9 \cdot 9}{90}$

Step 2

Combine the numerators over the common denominator.

$\frac{- 2 \cdot 30 + 7 \cdot 10 - 9 \cdot 9}{90}$

Step 3

Simplify each term.

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Step 3.1

Multiply $- 2$ by $30$ .

$\frac{- 60 + 7 \cdot 10 - 9 \cdot 9}{90}$

Step 3.2

Multiply $7$ by $10$ .

$\frac{- 60 + 70 - 9 \cdot 9}{90}$

Step 3.3

Multiply $- 9$ by $9$ .

$\frac{- 60 + 70 - 81}{90}$

Step 4

Simplify the expression.

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Step 4.1

Add $- 60$ and $70$ .

$\frac{10 - 81}{90}$

Step 4.2

Subtract $81$ from $10$ .

$\frac{- 71}{90}$

Step 4.3

Move the negative in front of the fraction.

$- \frac{71}{90}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{71}{90}$

Decimal Form:

$- 0.7\overline{8}$