Finite Math Examples

$\frac{6}{36} + \frac{12}{36} - \frac{5}{18}$

Step 1

Combine fractions.

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Step 1.1

Combine the numerators over the common denominator.

$\frac{6 + 12}{36} + \frac{- 5}{18}$

Step 1.2

Add $6$ and $12$ .

$\frac{18}{36} + \frac{- 5}{18}$

Step 2

Simplify each term.

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Step 2.1

Cancel the common factor of $18$ and $36$ .

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Step 2.1.1

Factor $18$ out of $18$ .

$\frac{18 (1)}{36} + \frac{- 5}{18}$

Step 2.1.2

Cancel the common factors.

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Step 2.1.2.1

Factor $18$ out of $36$ .

$\frac{18 \cdot 1}{18 \cdot 2} + \frac{- 5}{18}$

Step 2.1.2.2

Cancel the common factor.

$\frac{18 \cdot 1}{18 \cdot 2} + \frac{- 5}{18}$

Step 2.1.2.3

Rewrite the expression.

$\frac{1}{2} + \frac{- 5}{18}$

Step 2.2

Move the negative in front of the fraction.

$\frac{1}{2} - \frac{5}{18}$

Step 3

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{1}{2} \cdot \frac{9}{9} - \frac{5}{18}$

Step 4

Write each expression with a common denominator of $18$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

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

$\frac{9}{2 \cdot 9} - \frac{5}{18}$

Step 4.2

Multiply $2$ by $9$ .

$\frac{9}{18} - \frac{5}{18}$

Step 5

Simplify the expression.

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Step 5.1

Combine the numerators over the common denominator.

$\frac{9 - 5}{18}$

Step 5.2

Subtract $5$ from $9$ .

$\frac{4}{18}$

Step 6

Cancel the common factor of $4$ and $18$ .

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Step 6.1

Factor $2$ out of $4$ .

$\frac{2 (2)}{18}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $2$ out of $18$ .

$\frac{2 \cdot 2}{2 \cdot 9}$

Step 6.2.2

Cancel the common factor.

$\frac{2 \cdot 2}{2 \cdot 9}$

Step 6.2.3

Rewrite the expression.

$\frac{2}{9}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{2}{9}$

Decimal Form:

$0.\overline{2}$