Finite Math Examples

$0 \cdot \frac{1}{3} + 1 \cdot \frac{8}{15} + 2 \frac{2}{15}$

Step 1

Convert $2 \frac{2}{15}$ to an improper fraction.

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Step 1.1

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

$0 \cdot \frac{1}{3} + 1 \cdot \frac{8}{15} + 2 + \frac{2}{15}$

Step 1.2

Add $2$ and $\frac{2}{15}$ .

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Step 1.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{15}{15}$ .

$0 \cdot \frac{1}{3} + 1 \cdot \frac{8}{15} + 2 \cdot \frac{15}{15} + \frac{2}{15}$

Step 1.2.2

Combine $2$ and $\frac{15}{15}$ .

$0 \cdot \frac{1}{3} + 1 \cdot \frac{8}{15} + \frac{2 \cdot 15}{15} + \frac{2}{15}$

Step 1.2.3

Combine the numerators over the common denominator.

$0 \cdot \frac{1}{3} + 1 \cdot \frac{8}{15} + \frac{2 \cdot 15 + 2}{15}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $2$ by $15$ .

$0 \cdot \frac{1}{3} + 1 \cdot \frac{8}{15} + \frac{30 + 2}{15}$

Step 1.2.4.2

Add $30$ and $2$ .

$0 \cdot \frac{1}{3} + 1 \cdot \frac{8}{15} + \frac{32}{15}$

Step 2

Simplify each term.

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Step 2.1

Multiply $0$ by $\frac{1}{3}$ .

$0 + 1 \cdot \frac{8}{15} + \frac{32}{15}$

Step 2.2

Multiply $\frac{8}{15}$ by $1$ .

$0 + \frac{8}{15} + \frac{32}{15}$

Step 3

Simplify terms.

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Step 3.1

Combine the numerators over the common denominator.

$\frac{8 + 32}{15}$

Step 3.2

Add $8$ and $32$ .

$\frac{40}{15}$

Step 3.3

Cancel the common factor of $40$ and $15$ .

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Step 3.3.1

Factor $5$ out of $40$ .

$\frac{5 (8)}{15}$

Step 3.3.2

Cancel the common factors.

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Step 3.3.2.1

Factor $5$ out of $15$ .

$\frac{5 \cdot 8}{5 \cdot 3}$

Step 3.3.2.2

Cancel the common factor.

$\frac{5 \cdot 8}{5 \cdot 3}$

Step 3.3.2.3

Rewrite the expression.

$\frac{8}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{8}{3}$

Decimal Form:

$2.\overline{6}$

Mixed Number Form:

$2 \frac{2}{3}$