Finite Math Examples

$13 \frac{1}{2} - 24 - 5$

Step 1

Convert $13 \frac{1}{2}$ to an improper fraction.

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Step 1.1

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

$13 + \frac{1}{2} - 24 - 5$

Step 1.2

Add $13$ and $\frac{1}{2}$ .

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Step 1.2.1

To write $13$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$13 \cdot \frac{2}{2} + \frac{1}{2} - 24 - 5$

Step 1.2.2

Combine $13$ and $\frac{2}{2}$ .

$\frac{13 \cdot 2}{2} + \frac{1}{2} - 24 - 5$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{13 \cdot 2 + 1}{2} - 24 - 5$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $13$ by $2$ .

$\frac{26 + 1}{2} - 24 - 5$

Step 1.2.4.2

Add $26$ and $1$ .

$\frac{27}{2} - 24 - 5$

Step 2

Find the common denominator.

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Step 2.1

Write $- 24$ as a fraction with denominator $1$ .

$\frac{27}{2} + \frac{- 24}{1} - 5$

Step 2.2

Multiply $\frac{- 24}{1}$ by $\frac{2}{2}$ .

$\frac{27}{2} + \frac{- 24}{1} \cdot \frac{2}{2} - 5$

Step 2.3

Multiply $\frac{- 24}{1}$ by $\frac{2}{2}$ .

$\frac{27}{2} + \frac{- 24 \cdot 2}{2} - 5$

Step 2.4

Write $- 5$ as a fraction with denominator $1$ .

$\frac{27}{2} + \frac{- 24 \cdot 2}{2} + \frac{- 5}{1}$

Step 2.5

Multiply $\frac{- 5}{1}$ by $\frac{2}{2}$ .

$\frac{27}{2} + \frac{- 24 \cdot 2}{2} + \frac{- 5}{1} \cdot \frac{2}{2}$

Step 2.6

Multiply $\frac{- 5}{1}$ by $\frac{2}{2}$ .

$\frac{27}{2} + \frac{- 24 \cdot 2}{2} + \frac{- 5 \cdot 2}{2}$

Step 3

Combine the numerators over the common denominator.

$\frac{27 - 24 \cdot 2 - 5 \cdot 2}{2}$

Step 4

Simplify each term.

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Step 4.1

Multiply $- 24$ by $2$ .

$\frac{27 - 48 - 5 \cdot 2}{2}$

Step 4.2

Multiply $- 5$ by $2$ .

$\frac{27 - 48 - 10}{2}$

Step 5

Simplify the expression.

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Step 5.1

Subtract $48$ from $27$ .

$\frac{- 21 - 10}{2}$

Step 5.2

Subtract $10$ from $- 21$ .

$\frac{- 31}{2}$

Step 5.3

Move the negative in front of the fraction.

$- \frac{31}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \frac{31}{2}$

Decimal Form:

$- 15.5$

Mixed Number Form:

$- 15 \frac{1}{2}$