Finite Math Examples

$a - 8 = 11 \frac{1}{2}$

Step 1

Simplify the right side.

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Step 1.1

Convert $11 \frac{1}{2}$ to an improper fraction.

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Step 1.1.1

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

$a - 8 = 11 + \frac{1}{2}$

Step 1.1.2

Add $11$ and $\frac{1}{2}$ .

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Step 1.1.2.1

To write $11$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$a - 8 = 11 \cdot \frac{2}{2} + \frac{1}{2}$

Step 1.1.2.2

Combine $11$ and $\frac{2}{2}$ .

$a - 8 = \frac{11 \cdot 2}{2} + \frac{1}{2}$

Step 1.1.2.3

Combine the numerators over the common denominator.

$a - 8 = \frac{11 \cdot 2 + 1}{2}$

Step 1.1.2.4

Simplify the numerator.

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Step 1.1.2.4.1

Multiply $11$ by $2$ .

$a - 8 = \frac{22 + 1}{2}$

Step 1.1.2.4.2

Add $22$ and $1$ .

$a - 8 = \frac{23}{2}$

Step 2

Move all terms not containing $a$ to the right side of the equation.

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Step 2.1

Add $8$ to both sides of the equation.

$a = \frac{23}{2} + 8$

Step 2.2

To write $8$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$a = \frac{23}{2} + 8 \cdot \frac{2}{2}$

Step 2.3

Combine $8$ and $\frac{2}{2}$ .

$a = \frac{23}{2} + \frac{8 \cdot 2}{2}$

Step 2.4

Combine the numerators over the common denominator.

$a = \frac{23 + 8 \cdot 2}{2}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $8$ by $2$ .

$a = \frac{23 + 16}{2}$

Step 2.5.2

Add $23$ and $16$ .

$a = \frac{39}{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$a = \frac{39}{2}$

Decimal Form:

$a = 19.5$

Mixed Number Form:

$a = 19 \frac{1}{2}$