Finite Math Examples

$\frac{5}{9} + \frac{4}{8} - \frac{4}{9}$

Step 1

Combine the numerators over the common denominator.

$\frac{5 - 4}{9} + \frac{4}{8}$

Step 2

Subtract $4$ from $5$ .

$\frac{1}{9} + \frac{4}{8}$

Step 3

Cancel the common factor of $4$ and $8$ .

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Step 3.1

Factor $4$ out of $4$ .

$\frac{1}{9} + \frac{4 (1)}{8}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $4$ out of $8$ .

$\frac{1}{9} + \frac{4 \cdot 1}{4 \cdot 2}$

Step 3.2.2

Cancel the common factor.

$\frac{1}{9} + \frac{4 \cdot 1}{4 \cdot 2}$

Step 3.2.3

Rewrite the expression.

$\frac{1}{9} + \frac{1}{2}$

Step 4

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

$\frac{1}{9} \cdot \frac{2}{2} + \frac{1}{2}$

Step 5

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

$\frac{1}{9} \cdot \frac{2}{2} + \frac{1}{2} \cdot \frac{9}{9}$

Step 6

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

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Step 6.1

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

$\frac{2}{9 \cdot 2} + \frac{1}{2} \cdot \frac{9}{9}$

Step 6.2

Multiply $9$ by $2$ .

$\frac{2}{18} + \frac{1}{2} \cdot \frac{9}{9}$

Step 6.3

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

$\frac{2}{18} + \frac{9}{2 \cdot 9}$

Step 6.4

Multiply $2$ by $9$ .

$\frac{2}{18} + \frac{9}{18}$

Step 7

Combine the numerators over the common denominator.

$\frac{2 + 9}{18}$

Step 8

Add $2$ and $9$ .

$\frac{11}{18}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{11}{18}$

Decimal Form:

$0.6\overline{1}$