Algebra Examples

$12 \frac{1}{2} - (- 4 \frac{1}{2})$

Step 1

Convert $12 \frac{1}{2}$ to an improper fraction.

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Step 1.1

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

$12 + \frac{1}{2} - (- 4 \frac{1}{2})$

Step 1.2

Add $12$ and $\frac{1}{2}$ .

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Step 1.2.1

To write $12$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$12 \cdot \frac{2}{2} + \frac{1}{2} - (- 4 \frac{1}{2})$

Step 1.2.2

Combine $12$ and $\frac{2}{2}$ .

$\frac{12 \cdot 2}{2} + \frac{1}{2} - (- 4 \frac{1}{2})$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{12 \cdot 2 + 1}{2} - (- 4 \frac{1}{2})$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $12$ by $2$ .

$\frac{24 + 1}{2} - (- 4 \frac{1}{2})$

Step 1.2.4.2

Add $24$ and $1$ .

$\frac{25}{2} - (- 4 \frac{1}{2})$

Step 2

Convert $4 \frac{1}{2}$ to an improper fraction.

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Step 2.1

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

$\frac{25}{2} - - (4 + \frac{1}{2})$

Step 2.2

Add $4$ and $\frac{1}{2}$ .

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Step 2.2.1

To write $4$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{25}{2} - - (4 \cdot \frac{2}{2} + \frac{1}{2})$

Step 2.2.2

Combine $4$ and $\frac{2}{2}$ .

$\frac{25}{2} - - (\frac{4 \cdot 2}{2} + \frac{1}{2})$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{25}{2} - - \frac{4 \cdot 2 + 1}{2}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $4$ by $2$ .

$\frac{25}{2} - - \frac{8 + 1}{2}$

Step 2.2.4.2

Add $8$ and $1$ .

$\frac{25}{2} - - \frac{9}{2}$

Step 3

Multiply $- - \frac{9}{2}$ .

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Step 3.1

Multiply $- 1$ by $- 1$ .

$\frac{25}{2} + 1 (\frac{9}{2})$

Step 3.2

Multiply $\frac{9}{2}$ by $1$ .

$\frac{25}{2} + \frac{9}{2}$

Step 4

Combine the numerators over the common denominator.

$\frac{25 + 9}{2}$

Step 5

Simplify the expression.

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Step 5.1

Add $25$ and $9$ .

$\frac{34}{2}$

Step 5.2

Divide $34$ by $2$ .

$17$