Trigonometry Examples

$\frac{1}{2} + (- \frac{4}{8}) = 2 \frac{1}{2}$

Step 1

Simplify the left side.

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Step 1.1

Simplify $\frac{1}{2} - \frac{4}{8}$ .

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Step 1.1.1

Cancel the common factor of $4$ and $8$ .

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Step 1.1.1.1

Factor $4$ out of $4$ .

$\frac{1}{2} - \frac{4 (1)}{8} = 2 \frac{1}{2}$

Step 1.1.1.2

Cancel the common factors.

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Step 1.1.1.2.1

Factor $4$ out of $8$ .

$\frac{1}{2} - \frac{4 \cdot 1}{4 \cdot 2} = 2 \frac{1}{2}$

Step 1.1.1.2.2

Cancel the common factor.

$\frac{1}{2} - \frac{4 \cdot 1}{4 \cdot 2} = 2 \frac{1}{2}$

Step 1.1.1.2.3

Rewrite the expression.

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

Step 1.1.2

Combine the numerators over the common denominator.

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

Step 1.1.3

Simplify the expression.

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Step 1.1.3.1

Subtract $1$ from $1$ .

$\frac{0}{2} = 2 \frac{1}{2}$

Step 1.1.3.2

Divide $0$ by $2$ .

$0 = 2 \frac{1}{2}$

Step 2

Simplify the right side.

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Step 2.1

Convert $2 \frac{1}{2}$ to an improper fraction.

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Step 2.1.1

A mixed number is an addition of its whole and fractional parts.

$0 = 2 + \frac{1}{2}$

Step 2.1.2

Add $2$ and $\frac{1}{2}$ .

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Step 2.1.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$0 = 2 \cdot \frac{2}{2} + \frac{1}{2}$

Step 2.1.2.2

Combine $2$ and $\frac{2}{2}$ .

$0 = \frac{2 \cdot 2}{2} + \frac{1}{2}$

Step 2.1.2.3

Combine the numerators over the common denominator.

$0 = \frac{2 \cdot 2 + 1}{2}$

Step 2.1.2.4

Simplify the numerator.

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Step 2.1.2.4.1

Multiply $2$ by $2$ .

$0 = \frac{4 + 1}{2}$

Step 2.1.2.4.2

Add $4$ and $1$ .

$0 = \frac{5}{2}$

Step 3

Set the numerator equal to zero.

$5 = 0$

Step 4

Since $5 \neq 0$ , there are no solutions.

No solution