Finite Math Examples

$- 3 + 1 - \frac{1}{3} + \frac{1}{9}$

Step 1

Find the common denominator.

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Step 1.1

Write $- 3$ as a fraction with denominator $1$ .

$\frac{- 3}{1} + 1 - \frac{1}{3} + \frac{1}{9}$

Step 1.2

Multiply $\frac{- 3}{1}$ by $\frac{9}{9}$ .

$\frac{- 3}{1} \cdot \frac{9}{9} + 1 - \frac{1}{3} + \frac{1}{9}$

Step 1.3

Multiply $\frac{- 3}{1}$ by $\frac{9}{9}$ .

$\frac{- 3 \cdot 9}{9} + 1 - \frac{1}{3} + \frac{1}{9}$

Step 1.4

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

$\frac{- 3 \cdot 9}{9} + \frac{1}{1} - \frac{1}{3} + \frac{1}{9}$

Step 1.5

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

$\frac{- 3 \cdot 9}{9} + \frac{1}{1} \cdot \frac{9}{9} - \frac{1}{3} + \frac{1}{9}$

Step 1.6

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

$\frac{- 3 \cdot 9}{9} + \frac{9}{9} - \frac{1}{3} + \frac{1}{9}$

Step 1.7

Multiply $\frac{1}{3}$ by $\frac{3}{3}$ .

$\frac{- 3 \cdot 9}{9} + \frac{9}{9} - (\frac{1}{3} \cdot \frac{3}{3}) + \frac{1}{9}$

Step 1.8

Multiply $\frac{1}{3}$ by $\frac{3}{3}$ .

$\frac{- 3 \cdot 9}{9} + \frac{9}{9} - \frac{3}{3 \cdot 3} + \frac{1}{9}$

Step 1.9

Multiply $3$ by $3$ .

$\frac{- 3 \cdot 9}{9} + \frac{9}{9} - \frac{3}{9} + \frac{1}{9}$

Step 2

Combine the numerators over the common denominator.

$\frac{- 3 \cdot 9 + 9 - 3 + 1}{9}$

Step 3

Simplify the expression.

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Step 3.1

Multiply $- 3$ by $9$ .

$\frac{- 27 + 9 - 3 + 1}{9}$

Step 3.2

Add $- 27$ and $9$ .

$\frac{- 18 - 3 + 1}{9}$

Step 3.3

Subtract $3$ from $- 18$ .

$\frac{- 21 + 1}{9}$

Step 3.4

Add $- 21$ and $1$ .

$\frac{- 20}{9}$

Step 3.5

Move the negative in front of the fraction.

$- \frac{20}{9}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- \frac{20}{9}$

Decimal Form:

$- 2.\overline{2}$

Mixed Number Form:

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