Trigonometry Examples

$\frac{- \frac{12}{13}}{1 - \frac{5}{13}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$- \frac{12}{13} \cdot \frac{1}{1 - \frac{5}{13}}$

Step 2

Simplify the denominator.

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Step 2.1

Write $1$ as a fraction with a common denominator.

$- \frac{12}{13} \cdot \frac{1}{\frac{13}{13} - \frac{5}{13}}$

Step 2.2

Combine the numerators over the common denominator.

$- \frac{12}{13} \cdot \frac{1}{\frac{13 - 5}{13}}$

Step 2.3

Subtract $5$ from $13$ .

$- \frac{12}{13} \cdot \frac{1}{\frac{8}{13}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$- \frac{12}{13} (1 (\frac{13}{8}))$

Step 4

Multiply $\frac{13}{8}$ by $1$ .

$- \frac{12}{13} \cdot \frac{13}{8}$

Step 5

Cancel the common factor of $4$ .

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Step 5.1

Move the leading negative in $- \frac{12}{13}$ into the numerator.

$\frac{- 12}{13} \cdot \frac{13}{8}$

Step 5.2

Factor $4$ out of $- 12$ .

$\frac{4 (- 3)}{13} \cdot \frac{13}{8}$

Step 5.3

Factor $4$ out of $8$ .

$\frac{4 \cdot - 3}{13} \cdot \frac{13}{4 \cdot 2}$

Step 5.4

Cancel the common factor.

$\frac{4 \cdot - 3}{13} \cdot \frac{13}{4 \cdot 2}$

Step 5.5

Rewrite the expression.

$\frac{- 3}{13} \cdot \frac{13}{2}$

Step 6

Cancel the common factor of $13$ .

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Step 6.1

Cancel the common factor.

$\frac{- 3}{13} \cdot \frac{13}{2}$

Step 6.2

Rewrite the expression.

$- 3 (\frac{1}{2})$

Step 7

Combine $- 3$ and $\frac{1}{2}$ .

$\frac{- 3}{2}$

Step 8

Move the negative in front of the fraction.

$- \frac{3}{2}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$- \frac{3}{2}$

Decimal Form:

$- 1.5$

Mixed Number Form:

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