Finite Math Examples

$\frac{1}{2} \cdot 10 + \frac{1}{3} \cdot 1 + \frac{1}{3} + 5$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $2$ .

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Step 1.1.1

Factor $2$ out of $10$ .

$\frac{1}{2} \cdot (2 (5)) + \frac{1}{3} \cdot 1 + \frac{1}{3} + 5$

Step 1.1.2

Cancel the common factor.

$\frac{1}{2} \cdot (2 \cdot 5) + \frac{1}{3} \cdot 1 + \frac{1}{3} + 5$

Step 1.1.3

Rewrite the expression.

$5 + \frac{1}{3} \cdot 1 + \frac{1}{3} + 5$

Step 1.2

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

$5 + \frac{1}{3} + \frac{1}{3} + 5$

Step 2

Combine fractions.

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Step 2.1

Combine the numerators over the common denominator.

$5 + 5 + \frac{1 + 1}{3}$

Step 2.2

Add $1$ and $1$ .

$5 + 5 + \frac{2}{3}$

Step 3

Find the common denominator.

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Step 3.1

Write $5$ as a fraction with denominator $1$ .

$\frac{5}{1} + 5 + \frac{2}{3}$

Step 3.2

Multiply $\frac{5}{1}$ by $\frac{3}{3}$ .

$\frac{5}{1} \cdot \frac{3}{3} + 5 + \frac{2}{3}$

Step 3.3

Multiply $\frac{5}{1}$ by $\frac{3}{3}$ .

$\frac{5 \cdot 3}{3} + 5 + \frac{2}{3}$

Step 3.4

Write $5$ as a fraction with denominator $1$ .

$\frac{5 \cdot 3}{3} + \frac{5}{1} + \frac{2}{3}$

Step 3.5

Multiply $\frac{5}{1}$ by $\frac{3}{3}$ .

$\frac{5 \cdot 3}{3} + \frac{5}{1} \cdot \frac{3}{3} + \frac{2}{3}$

Step 3.6

Multiply $\frac{5}{1}$ by $\frac{3}{3}$ .

$\frac{5 \cdot 3}{3} + \frac{5 \cdot 3}{3} + \frac{2}{3}$

Step 4

Combine the numerators over the common denominator.

$\frac{5 \cdot 3 + 5 \cdot 3 + 2}{3}$

Step 5

Simplify each term.

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Step 5.1

Multiply $5$ by $3$ .

$\frac{15 + 5 \cdot 3 + 2}{3}$

Step 5.2

Multiply $5$ by $3$ .

$\frac{15 + 15 + 2}{3}$

Step 6

Simplify by adding numbers.

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Step 6.1

Add $15$ and $15$ .

$\frac{30 + 2}{3}$

Step 6.2

Add $30$ and $2$ .

$\frac{32}{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{32}{3}$

Decimal Form:

$10.\overline{6}$

Mixed Number Form:

$10 \frac{2}{3}$