Finite Math Examples

$18 - 9 + \frac{9}{2} - \frac{9}{4} + \frac{9}{8}$

Step 1

Find the common denominator.

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Step 1.1

Write $18$ as a fraction with denominator $1$ .

$\frac{18}{1} - 9 + \frac{9}{2} - \frac{9}{4} + \frac{9}{8}$

Step 1.2

Multiply $\frac{18}{1}$ by $\frac{8}{8}$ .

$\frac{18}{1} \cdot \frac{8}{8} - 9 + \frac{9}{2} - \frac{9}{4} + \frac{9}{8}$

Step 1.3

Multiply $\frac{18}{1}$ by $\frac{8}{8}$ .

$\frac{18 \cdot 8}{8} - 9 + \frac{9}{2} - \frac{9}{4} + \frac{9}{8}$

Step 1.4

Write $- 9$ as a fraction with denominator $1$ .

$\frac{18 \cdot 8}{8} + \frac{- 9}{1} + \frac{9}{2} - \frac{9}{4} + \frac{9}{8}$

Step 1.5

Multiply $\frac{- 9}{1}$ by $\frac{8}{8}$ .

$\frac{18 \cdot 8}{8} + \frac{- 9}{1} \cdot \frac{8}{8} + \frac{9}{2} - \frac{9}{4} + \frac{9}{8}$

Step 1.6

Multiply $\frac{- 9}{1}$ by $\frac{8}{8}$ .

$\frac{18 \cdot 8}{8} + \frac{- 9 \cdot 8}{8} + \frac{9}{2} - \frac{9}{4} + \frac{9}{8}$

Step 1.7

Multiply $\frac{9}{2}$ by $\frac{4}{4}$ .

$\frac{18 \cdot 8}{8} + \frac{- 9 \cdot 8}{8} + \frac{9}{2} \cdot \frac{4}{4} - \frac{9}{4} + \frac{9}{8}$

Step 1.8

Multiply $\frac{9}{2}$ by $\frac{4}{4}$ .

$\frac{18 \cdot 8}{8} + \frac{- 9 \cdot 8}{8} + \frac{9 \cdot 4}{2 \cdot 4} - \frac{9}{4} + \frac{9}{8}$

Step 1.9

Multiply $\frac{9}{4}$ by $\frac{2}{2}$ .

$\frac{18 \cdot 8}{8} + \frac{- 9 \cdot 8}{8} + \frac{9 \cdot 4}{2 \cdot 4} - (\frac{9}{4} \cdot \frac{2}{2}) + \frac{9}{8}$

Step 1.10

Multiply $\frac{9}{4}$ by $\frac{2}{2}$ .

$\frac{18 \cdot 8}{8} + \frac{- 9 \cdot 8}{8} + \frac{9 \cdot 4}{2 \cdot 4} - \frac{9 \cdot 2}{4 \cdot 2} + \frac{9}{8}$

Step 1.11

Multiply $2$ by $4$ .

$\frac{18 \cdot 8}{8} + \frac{- 9 \cdot 8}{8} + \frac{9 \cdot 4}{8} - \frac{9 \cdot 2}{4 \cdot 2} + \frac{9}{8}$

Step 1.12

Reorder the factors of $4 \cdot 2$ .

$\frac{18 \cdot 8}{8} + \frac{- 9 \cdot 8}{8} + \frac{9 \cdot 4}{8} - \frac{9 \cdot 2}{2 \cdot 4} + \frac{9}{8}$

Step 1.13

Multiply $2$ by $4$ .

$\frac{18 \cdot 8}{8} + \frac{- 9 \cdot 8}{8} + \frac{9 \cdot 4}{8} - \frac{9 \cdot 2}{8} + \frac{9}{8}$

Step 2

Combine the numerators over the common denominator.

$\frac{18 \cdot 8 - 9 \cdot 8 + 9 \cdot 4 - 9 \cdot 2 + 9}{8}$

Step 3

Simplify each term.

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Step 3.1

Multiply $18$ by $8$ .

$\frac{144 - 9 \cdot 8 + 9 \cdot 4 - 9 \cdot 2 + 9}{8}$

Step 3.2

Multiply $- 9$ by $8$ .

$\frac{144 - 72 + 9 \cdot 4 - 9 \cdot 2 + 9}{8}$

Step 3.3

Multiply $9$ by $4$ .

$\frac{144 - 72 + 36 - 9 \cdot 2 + 9}{8}$

Step 3.4

Multiply $- 9$ by $2$ .

$\frac{144 - 72 + 36 - 18 + 9}{8}$

Step 4

Simplify by adding and subtracting.

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Step 4.1

Subtract $72$ from $144$ .

$\frac{72 + 36 - 18 + 9}{8}$

Step 4.2

Add $72$ and $36$ .

$\frac{108 - 18 + 9}{8}$

Step 4.3

Subtract $18$ from $108$ .

$\frac{90 + 9}{8}$

Step 4.4

Add $90$ and $9$ .

$\frac{99}{8}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{99}{8}$

Decimal Form:

$12.375$

Mixed Number Form:

$12 \frac{3}{8}$