Finite Math Examples

$\frac{2}{14} \cdot \frac{1}{13} + \frac{6}{14} \cdot \frac{5}{13} + \frac{6}{14} \cdot \frac{5}{13}$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $2$ and $14$ .

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Step 1.1.1

Factor $2$ out of $2$ .

$\frac{2 (1)}{14} \cdot \frac{1}{13} + \frac{6}{14} \cdot \frac{5}{13} + \frac{6}{14} \cdot \frac{5}{13}$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $2$ out of $14$ .

$\frac{2 \cdot 1}{2 \cdot 7} \cdot \frac{1}{13} + \frac{6}{14} \cdot \frac{5}{13} + \frac{6}{14} \cdot \frac{5}{13}$

Step 1.1.2.2

Cancel the common factor.

$\frac{2 \cdot 1}{2 \cdot 7} \cdot \frac{1}{13} + \frac{6}{14} \cdot \frac{5}{13} + \frac{6}{14} \cdot \frac{5}{13}$

Step 1.1.2.3

Rewrite the expression.

$\frac{1}{7} \cdot \frac{1}{13} + \frac{6}{14} \cdot \frac{5}{13} + \frac{6}{14} \cdot \frac{5}{13}$

Step 1.2

Multiply $\frac{1}{7} \cdot \frac{1}{13}$ .

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Step 1.2.1

Multiply $\frac{1}{7}$ by $\frac{1}{13}$ .

$\frac{1}{7 \cdot 13} + \frac{6}{14} \cdot \frac{5}{13} + \frac{6}{14} \cdot \frac{5}{13}$

Step 1.2.2

Multiply $7$ by $13$ .

$\frac{1}{91} + \frac{6}{14} \cdot \frac{5}{13} + \frac{6}{14} \cdot \frac{5}{13}$

Step 1.3

Cancel the common factor of $6$ and $14$ .

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Step 1.3.1

Factor $2$ out of $6$ .

$\frac{1}{91} + \frac{2 (3)}{14} \cdot \frac{5}{13} + \frac{6}{14} \cdot \frac{5}{13}$

Step 1.3.2

Cancel the common factors.

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Step 1.3.2.1

Factor $2$ out of $14$ .

$\frac{1}{91} + \frac{2 \cdot 3}{2 \cdot 7} \cdot \frac{5}{13} + \frac{6}{14} \cdot \frac{5}{13}$

Step 1.3.2.2

Cancel the common factor.

$\frac{1}{91} + \frac{2 \cdot 3}{2 \cdot 7} \cdot \frac{5}{13} + \frac{6}{14} \cdot \frac{5}{13}$

Step 1.3.2.3

Rewrite the expression.

$\frac{1}{91} + \frac{3}{7} \cdot \frac{5}{13} + \frac{6}{14} \cdot \frac{5}{13}$

Step 1.4

Multiply $\frac{3}{7} \cdot \frac{5}{13}$ .

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Step 1.4.1

Multiply $\frac{3}{7}$ by $\frac{5}{13}$ .

$\frac{1}{91} + \frac{3 \cdot 5}{7 \cdot 13} + \frac{6}{14} \cdot \frac{5}{13}$

Step 1.4.2

Multiply $3$ by $5$ .

$\frac{1}{91} + \frac{15}{7 \cdot 13} + \frac{6}{14} \cdot \frac{5}{13}$

Step 1.4.3

Multiply $7$ by $13$ .

$\frac{1}{91} + \frac{15}{91} + \frac{6}{14} \cdot \frac{5}{13}$

Step 1.5

Cancel the common factor of $6$ and $14$ .

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Step 1.5.1

Factor $2$ out of $6$ .

$\frac{1}{91} + \frac{15}{91} + \frac{2 (3)}{14} \cdot \frac{5}{13}$

Step 1.5.2

Cancel the common factors.

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Step 1.5.2.1

Factor $2$ out of $14$ .

$\frac{1}{91} + \frac{15}{91} + \frac{2 \cdot 3}{2 \cdot 7} \cdot \frac{5}{13}$

Step 1.5.2.2

Cancel the common factor.

$\frac{1}{91} + \frac{15}{91} + \frac{2 \cdot 3}{2 \cdot 7} \cdot \frac{5}{13}$

Step 1.5.2.3

Rewrite the expression.

$\frac{1}{91} + \frac{15}{91} + \frac{3}{7} \cdot \frac{5}{13}$

Step 1.6

Multiply $\frac{3}{7} \cdot \frac{5}{13}$ .

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Step 1.6.1

Multiply $\frac{3}{7}$ by $\frac{5}{13}$ .

$\frac{1}{91} + \frac{15}{91} + \frac{3 \cdot 5}{7 \cdot 13}$

Step 1.6.2

Multiply $3$ by $5$ .

$\frac{1}{91} + \frac{15}{91} + \frac{15}{7 \cdot 13}$

Step 1.6.3

Multiply $7$ by $13$ .

$\frac{1}{91} + \frac{15}{91} + \frac{15}{91}$

Step 2

Combine fractions.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{1 + 15 + 15}{91}$

Step 2.2

Simplify by adding numbers.

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Step 2.2.1

Add $1$ and $15$ .

$\frac{16 + 15}{91}$

Step 2.2.2

Add $16$ and $15$ .

$\frac{31}{91}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{31}{91}$

Decimal Form:

$0.\overline{340659}$