Trigonometry Examples

$\frac{5}{13} \cdot \frac{7}{25} - \frac{12}{13} \cdot \frac{24}{25}$

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

Factor $5$ out of $25$ .

$\frac{5}{13} \cdot \frac{7}{5 (5)} - \frac{12}{13} \cdot \frac{24}{25}$

Step 1.1.2

Cancel the common factor.

$\frac{5}{13} \cdot \frac{7}{5 \cdot 5} - \frac{12}{13} \cdot \frac{24}{25}$

Step 1.1.3

Rewrite the expression.

$\frac{1}{13} \cdot \frac{7}{5} - \frac{12}{13} \cdot \frac{24}{25}$

Step 1.2

Multiply $\frac{1}{13}$ by $\frac{7}{5}$ .

$\frac{7}{13 \cdot 5} - \frac{12}{13} \cdot \frac{24}{25}$

Step 1.3

Multiply $13$ by $5$ .

$\frac{7}{65} - \frac{12}{13} \cdot \frac{24}{25}$

Step 1.4

Multiply $- \frac{12}{13} \cdot \frac{24}{25}$ .

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Step 1.4.1

Multiply $\frac{24}{25}$ by $\frac{12}{13}$ .

$\frac{7}{65} - \frac{24 \cdot 12}{25 \cdot 13}$

Step 1.4.2

Multiply $24$ by $12$ .

$\frac{7}{65} - \frac{288}{25 \cdot 13}$

Step 1.4.3

Multiply $25$ by $13$ .

$\frac{7}{65} - \frac{288}{325}$

Step 2

To write $\frac{7}{65}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{7}{65} \cdot \frac{5}{5} - \frac{288}{325}$

Step 3

Write each expression with a common denominator of $325$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{7}{65}$ by $\frac{5}{5}$ .

$\frac{7 \cdot 5}{65 \cdot 5} - \frac{288}{325}$

Step 3.2

Multiply $65$ by $5$ .

$\frac{7 \cdot 5}{325} - \frac{288}{325}$

Step 4

Combine the numerators over the common denominator.

$\frac{7 \cdot 5 - 288}{325}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $7$ by $5$ .

$\frac{35 - 288}{325}$

Step 5.2

Subtract $288$ from $35$ .

$\frac{- 253}{325}$

Step 6

Move the negative in front of the fraction.

$- \frac{253}{325}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{253}{325}$

Decimal Form:

$- 0.77846153 \dots$