Finite Math Examples

$100 (\frac{22}{65}) + 200 (\frac{12}{65}) + 300 (\frac{6}{65}) + 400 (\frac{1}{13}) + 500 (\frac{18}{65}) + 600 (\frac{2}{65})$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $5$ .

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Step 1.1.1

Factor $5$ out of $100$ .

$5 (20) \frac{22}{65} + 200 (\frac{12}{65}) + 300 (\frac{6}{65}) + 400 (\frac{1}{13}) + 500 (\frac{18}{65}) + 600 (\frac{2}{65})$

Step 1.1.2

Factor $5$ out of $65$ .

$5 \cdot 20 \frac{22}{5 \cdot 13} + 200 (\frac{12}{65}) + 300 (\frac{6}{65}) + 400 (\frac{1}{13}) + 500 (\frac{18}{65}) + 600 (\frac{2}{65})$

Step 1.1.3

Cancel the common factor.

$5 \cdot 20 \frac{22}{5 \cdot 13} + 200 (\frac{12}{65}) + 300 (\frac{6}{65}) + 400 (\frac{1}{13}) + 500 (\frac{18}{65}) + 600 (\frac{2}{65})$

Step 1.1.4

Rewrite the expression.

$20 (\frac{22}{13}) + 200 (\frac{12}{65}) + 300 (\frac{6}{65}) + 400 (\frac{1}{13}) + 500 (\frac{18}{65}) + 600 (\frac{2}{65})$

Step 1.2

Combine $20$ and $\frac{22}{13}$ .

$\frac{20 \cdot 22}{13} + 200 (\frac{12}{65}) + 300 (\frac{6}{65}) + 400 (\frac{1}{13}) + 500 (\frac{18}{65}) + 600 (\frac{2}{65})$

Step 1.3

Multiply $20$ by $22$ .

$\frac{440}{13} + 200 (\frac{12}{65}) + 300 (\frac{6}{65}) + 400 (\frac{1}{13}) + 500 (\frac{18}{65}) + 600 (\frac{2}{65})$

Step 1.4

Cancel the common factor of $5$ .

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Step 1.4.1

Factor $5$ out of $200$ .

$\frac{440}{13} + 5 (40) \frac{12}{65} + 300 (\frac{6}{65}) + 400 (\frac{1}{13}) + 500 (\frac{18}{65}) + 600 (\frac{2}{65})$

Step 1.4.2

Factor $5$ out of $65$ .

$\frac{440}{13} + 5 \cdot 40 \frac{12}{5 \cdot 13} + 300 (\frac{6}{65}) + 400 (\frac{1}{13}) + 500 (\frac{18}{65}) + 600 (\frac{2}{65})$

Step 1.4.3

Cancel the common factor.

$\frac{440}{13} + 5 \cdot 40 \frac{12}{5 \cdot 13} + 300 (\frac{6}{65}) + 400 (\frac{1}{13}) + 500 (\frac{18}{65}) + 600 (\frac{2}{65})$

Step 1.4.4

Rewrite the expression.

$\frac{440}{13} + 40 (\frac{12}{13}) + 300 (\frac{6}{65}) + 400 (\frac{1}{13}) + 500 (\frac{18}{65}) + 600 (\frac{2}{65})$

Step 1.5

Combine $40$ and $\frac{12}{13}$ .

$\frac{440}{13} + \frac{40 \cdot 12}{13} + 300 (\frac{6}{65}) + 400 (\frac{1}{13}) + 500 (\frac{18}{65}) + 600 (\frac{2}{65})$

Step 1.6

Multiply $40$ by $12$ .

$\frac{440}{13} + \frac{480}{13} + 300 (\frac{6}{65}) + 400 (\frac{1}{13}) + 500 (\frac{18}{65}) + 600 (\frac{2}{65})$

Step 1.7

Cancel the common factor of $5$ .

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Step 1.7.1

Factor $5$ out of $300$ .

$\frac{440}{13} + \frac{480}{13} + 5 (60) \frac{6}{65} + 400 (\frac{1}{13}) + 500 (\frac{18}{65}) + 600 (\frac{2}{65})$

Step 1.7.2

Factor $5$ out of $65$ .

$\frac{440}{13} + \frac{480}{13} + 5 \cdot 60 \frac{6}{5 \cdot 13} + 400 (\frac{1}{13}) + 500 (\frac{18}{65}) + 600 (\frac{2}{65})$

Step 1.7.3

Cancel the common factor.

$\frac{440}{13} + \frac{480}{13} + 5 \cdot 60 \frac{6}{5 \cdot 13} + 400 (\frac{1}{13}) + 500 (\frac{18}{65}) + 600 (\frac{2}{65})$

Step 1.7.4

Rewrite the expression.

$\frac{440}{13} + \frac{480}{13} + 60 (\frac{6}{13}) + 400 (\frac{1}{13}) + 500 (\frac{18}{65}) + 600 (\frac{2}{65})$

Step 1.8

Combine $60$ and $\frac{6}{13}$ .

$\frac{440}{13} + \frac{480}{13} + \frac{60 \cdot 6}{13} + 400 (\frac{1}{13}) + 500 (\frac{18}{65}) + 600 (\frac{2}{65})$

Step 1.9

Multiply $60$ by $6$ .

$\frac{440}{13} + \frac{480}{13} + \frac{360}{13} + 400 (\frac{1}{13}) + 500 (\frac{18}{65}) + 600 (\frac{2}{65})$

Step 1.10

Combine $400$ and $\frac{1}{13}$ .

$\frac{440}{13} + \frac{480}{13} + \frac{360}{13} + \frac{400}{13} + 500 (\frac{18}{65}) + 600 (\frac{2}{65})$

Step 1.11

Cancel the common factor of $5$ .

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Step 1.11.1

Factor $5$ out of $500$ .

$\frac{440}{13} + \frac{480}{13} + \frac{360}{13} + \frac{400}{13} + 5 (100) \frac{18}{65} + 600 (\frac{2}{65})$

Step 1.11.2

Factor $5$ out of $65$ .

$\frac{440}{13} + \frac{480}{13} + \frac{360}{13} + \frac{400}{13} + 5 \cdot 100 \frac{18}{5 \cdot 13} + 600 (\frac{2}{65})$

Step 1.11.3

Cancel the common factor.

$\frac{440}{13} + \frac{480}{13} + \frac{360}{13} + \frac{400}{13} + 5 \cdot 100 \frac{18}{5 \cdot 13} + 600 (\frac{2}{65})$

Step 1.11.4

Rewrite the expression.

$\frac{440}{13} + \frac{480}{13} + \frac{360}{13} + \frac{400}{13} + 100 (\frac{18}{13}) + 600 (\frac{2}{65})$

Step 1.12

Combine $100$ and $\frac{18}{13}$ .

$\frac{440}{13} + \frac{480}{13} + \frac{360}{13} + \frac{400}{13} + \frac{100 \cdot 18}{13} + 600 (\frac{2}{65})$

Step 1.13

Multiply $100$ by $18$ .

$\frac{440}{13} + \frac{480}{13} + \frac{360}{13} + \frac{400}{13} + \frac{1800}{13} + 600 (\frac{2}{65})$

Step 1.14

Cancel the common factor of $5$ .

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Step 1.14.1

Factor $5$ out of $600$ .

$\frac{440}{13} + \frac{480}{13} + \frac{360}{13} + \frac{400}{13} + \frac{1800}{13} + 5 (120) \frac{2}{65}$

Step 1.14.2

Factor $5$ out of $65$ .

$\frac{440}{13} + \frac{480}{13} + \frac{360}{13} + \frac{400}{13} + \frac{1800}{13} + 5 \cdot 120 \frac{2}{5 \cdot 13}$

Step 1.14.3

Cancel the common factor.

$\frac{440}{13} + \frac{480}{13} + \frac{360}{13} + \frac{400}{13} + \frac{1800}{13} + 5 \cdot 120 \frac{2}{5 \cdot 13}$

Step 1.14.4

Rewrite the expression.

$\frac{440}{13} + \frac{480}{13} + \frac{360}{13} + \frac{400}{13} + \frac{1800}{13} + 120 (\frac{2}{13})$

Step 1.15

Combine $120$ and $\frac{2}{13}$ .

$\frac{440}{13} + \frac{480}{13} + \frac{360}{13} + \frac{400}{13} + \frac{1800}{13} + \frac{120 \cdot 2}{13}$

Step 1.16

Multiply $120$ by $2$ .

$\frac{440}{13} + \frac{480}{13} + \frac{360}{13} + \frac{400}{13} + \frac{1800}{13} + \frac{240}{13}$

Step 2

Combine fractions.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{440 + 480 + 360 + 400 + 1800 + 240}{13}$

Step 2.2

Simplify by adding numbers.

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Step 2.2.1

Add $440$ and $480$ .

$\frac{920 + 360 + 400 + 1800 + 240}{13}$

Step 2.2.2

Add $920$ and $360$ .

$\frac{1280 + 400 + 1800 + 240}{13}$

Step 2.2.3

Add $1280$ and $400$ .

$\frac{1680 + 1800 + 240}{13}$

Step 2.2.4

Add $1680$ and $1800$ .

$\frac{3480 + 240}{13}$

Step 2.2.5

Add $3480$ and $240$ .

$\frac{3720}{13}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{3720}{13}$

Decimal Form:

$286.15384615 \dots$

Mixed Number Form:

$286 \frac{2}{13}$