Trigonometry Examples

$(\frac{4}{5}) (- \frac{5}{13}) + (\frac{3}{5}) (\frac{12}{13})$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $5$ .

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Step 1.1.1

Move the leading negative in $- \frac{5}{13}$ into the numerator.

$\frac{4}{5} \cdot \frac{- 5}{13} + (\frac{3}{5}) (\frac{12}{13})$

Step 1.1.2

Factor $5$ out of $- 5$ .

$\frac{4}{5} \cdot \frac{5 (- 1)}{13} + (\frac{3}{5}) (\frac{12}{13})$

Step 1.1.3

Cancel the common factor.

$\frac{4}{5} \cdot \frac{5 \cdot - 1}{13} + (\frac{3}{5}) (\frac{12}{13})$

Step 1.1.4

Rewrite the expression.

$4 (\frac{- 1}{13}) + (\frac{3}{5}) (\frac{12}{13})$

Step 1.2

Combine $4$ and $\frac{- 1}{13}$ .

$\frac{4 \cdot - 1}{13} + (\frac{3}{5}) (\frac{12}{13})$

Step 1.3

Multiply $4$ by $- 1$ .

$\frac{- 4}{13} + (\frac{3}{5}) (\frac{12}{13})$

Step 1.4

Move the negative in front of the fraction.

$- \frac{4}{13} + (\frac{3}{5}) (\frac{12}{13})$

Step 1.5

Multiply $(\frac{3}{5}) (\frac{12}{13})$ .

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Step 1.5.1

Multiply $\frac{3}{5}$ by $\frac{12}{13}$ .

$- \frac{4}{13} + \frac{3 \cdot 12}{5 \cdot 13}$

Step 1.5.2

Multiply $3$ by $12$ .

$- \frac{4}{13} + \frac{36}{5 \cdot 13}$

Step 1.5.3

Multiply $5$ by $13$ .

$- \frac{4}{13} + \frac{36}{65}$

Step 2

To write $- \frac{4}{13}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{4}{13} \cdot \frac{5}{5} + \frac{36}{65}$

Step 3

Write each expression with a common denominator of $65$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{4}{13}$ by $\frac{5}{5}$ .

$- \frac{4 \cdot 5}{13 \cdot 5} + \frac{36}{65}$

Step 3.2

Multiply $13$ by $5$ .

$- \frac{4 \cdot 5}{65} + \frac{36}{65}$

Step 4

Combine the numerators over the common denominator.

$\frac{- 4 \cdot 5 + 36}{65}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $- 4$ by $5$ .

$\frac{- 20 + 36}{65}$

Step 5.2

Add $- 20$ and $36$ .

$\frac{16}{65}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{16}{65}$

Decimal Form:

$0.2\overline{461538}$