Finite Math Examples

$9999.75 \cdot \frac{1}{10000} + 299.75 \cdot \frac{2}{10000} + 9.75 \cdot \frac{20}{10000} - 0.25 \cdot \frac{9977}{10000}$

Step 1

Simplify each term.

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Step 1.1

Combine $9999.75$ and $\frac{1}{10000}$ .

$\frac{9999.75}{10000} + 299.75 \cdot \frac{2}{10000} + 9.75 \cdot \frac{20}{10000} - 0.25 \cdot \frac{9977}{10000}$

Step 1.2

Divide $9999.75$ by $10000$ .

$0.999975 + 299.75 \cdot \frac{2}{10000} + 9.75 \cdot \frac{20}{10000} - 0.25 \cdot \frac{9977}{10000}$

Step 1.3

Cancel the common factor of $2$ and $10000$ .

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Step 1.3.1

Factor $2$ out of $2$ .

$0.999975 + 299.75 \cdot \frac{2 (1)}{10000} + 9.75 \cdot \frac{20}{10000} - 0.25 \cdot \frac{9977}{10000}$

Step 1.3.2

Cancel the common factors.

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Step 1.3.2.1

Factor $2$ out of $10000$ .

$0.999975 + 299.75 \cdot \frac{2 \cdot 1}{2 \cdot 5000} + 9.75 \cdot \frac{20}{10000} - 0.25 \cdot \frac{9977}{10000}$

Step 1.3.2.2

Cancel the common factor.

$0.999975 + 299.75 \cdot \frac{2 \cdot 1}{2 \cdot 5000} + 9.75 \cdot \frac{20}{10000} - 0.25 \cdot \frac{9977}{10000}$

Step 1.3.2.3

Rewrite the expression.

$0.999975 + 299.75 \cdot \frac{1}{5000} + 9.75 \cdot \frac{20}{10000} - 0.25 \cdot \frac{9977}{10000}$

Step 1.4

Combine $299.75$ and $\frac{1}{5000}$ .

$0.999975 + \frac{299.75}{5000} + 9.75 \cdot \frac{20}{10000} - 0.25 \cdot \frac{9977}{10000}$

Step 1.5

Divide $299.75$ by $5000$ .

$0.999975 + 0.05995 + 9.75 \cdot \frac{20}{10000} - 0.25 \cdot \frac{9977}{10000}$

Step 1.6

Cancel the common factor of $20$ and $10000$ .

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Step 1.6.1

Factor $20$ out of $20$ .

$0.999975 + 0.05995 + 9.75 \cdot \frac{20 (1)}{10000} - 0.25 \cdot \frac{9977}{10000}$

Step 1.6.2

Cancel the common factors.

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Step 1.6.2.1

Factor $20$ out of $10000$ .

$0.999975 + 0.05995 + 9.75 \cdot \frac{20 \cdot 1}{20 \cdot 500} - 0.25 \cdot \frac{9977}{10000}$

Step 1.6.2.2

Cancel the common factor.

$0.999975 + 0.05995 + 9.75 \cdot \frac{20 \cdot 1}{20 \cdot 500} - 0.25 \cdot \frac{9977}{10000}$

Step 1.6.2.3

Rewrite the expression.

$0.999975 + 0.05995 + 9.75 \cdot \frac{1}{500} - 0.25 \cdot \frac{9977}{10000}$

Step 1.7

Combine $9.75$ and $\frac{1}{500}$ .

$0.999975 + 0.05995 + \frac{9.75}{500} - 0.25 \cdot \frac{9977}{10000}$

Step 1.8

Divide $9.75$ by $500$ .

$0.999975 + 0.05995 + 0.0195 - 0.25 \cdot \frac{9977}{10000}$

Step 1.9

Cancel the common factor of $0.25$ .

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Step 1.9.1

Factor $0.25$ out of $- 0.25$ .

$0.999975 + 0.05995 + 0.0195 + 0.25 (- 1) \cdot \frac{9977}{10000}$

Step 1.9.2

Factor $0.25$ out of $10000$ .

$0.999975 + 0.05995 + 0.0195 + 0.25 \cdot - 1 \cdot \frac{9977}{0.25 \cdot 40000}$

Step 1.9.3

Cancel the common factor.

$0.999975 + 0.05995 + 0.0195 + 0.25 \cdot - 1 \cdot \frac{9977}{0.25 \cdot 40000}$

Step 1.9.4

Rewrite the expression.

$0.999975 + 0.05995 + 0.0195 - 1 \cdot \frac{9977}{40000}$

Step 1.10

Rewrite $- 1 (\frac{9977}{40000})$ as $- (\frac{9977}{40000})$ .

$0.999975 + 0.05995 + 0.0195 - \frac{9977}{40000}$

Step 2

Find the common denominator.

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Step 2.1

Write $0.999975$ as a fraction with denominator $1$ .

$\frac{0.999975}{1} + 0.05995 + 0.0195 - \frac{9977}{40000}$

Step 2.2

Multiply $\frac{0.999975}{1}$ by $\frac{40000}{40000}$ .

$\frac{0.999975}{1} \cdot \frac{40000}{40000} + 0.05995 + 0.0195 - \frac{9977}{40000}$

Step 2.3

Multiply $\frac{0.999975}{1}$ by $\frac{40000}{40000}$ .

$\frac{0.999975 \cdot 40000}{40000} + 0.05995 + 0.0195 - \frac{9977}{40000}$

Step 2.4

Write $0.05995$ as a fraction with denominator $1$ .

$\frac{0.999975 \cdot 40000}{40000} + \frac{0.05995}{1} + 0.0195 - \frac{9977}{40000}$

Step 2.5

Multiply $\frac{0.05995}{1}$ by $\frac{40000}{40000}$ .

$\frac{0.999975 \cdot 40000}{40000} + \frac{0.05995}{1} \cdot \frac{40000}{40000} + 0.0195 - \frac{9977}{40000}$

Step 2.6

Multiply $\frac{0.05995}{1}$ by $\frac{40000}{40000}$ .

$\frac{0.999975 \cdot 40000}{40000} + \frac{0.05995 \cdot 40000}{40000} + 0.0195 - \frac{9977}{40000}$

Step 2.7

Write $0.0195$ as a fraction with denominator $1$ .

$\frac{0.999975 \cdot 40000}{40000} + \frac{0.05995 \cdot 40000}{40000} + \frac{0.0195}{1} - \frac{9977}{40000}$

Step 2.8

Multiply $\frac{0.0195}{1}$ by $\frac{40000}{40000}$ .

$\frac{0.999975 \cdot 40000}{40000} + \frac{0.05995 \cdot 40000}{40000} + \frac{0.0195}{1} \cdot \frac{40000}{40000} - \frac{9977}{40000}$

Step 2.9

Multiply $\frac{0.0195}{1}$ by $\frac{40000}{40000}$ .

$\frac{0.999975 \cdot 40000}{40000} + \frac{0.05995 \cdot 40000}{40000} + \frac{0.0195 \cdot 40000}{40000} - \frac{9977}{40000}$

Step 3

Combine the numerators over the common denominator.

$\frac{0.999975 \cdot 40000 + 0.05995 \cdot 40000 + 0.0195 \cdot 40000 - 9977}{40000}$

Step 4

Simplify each term.

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Step 4.1

Multiply $0.999975$ by $40000$ .

$\frac{39999 + 0.05995 \cdot 40000 + 0.0195 \cdot 40000 - 9977}{40000}$

Step 4.2

Multiply $0.05995$ by $40000$ .

$\frac{39999 + 2398 + 0.0195 \cdot 40000 - 9977}{40000}$

Step 4.3

Multiply $0.0195$ by $40000$ .

$\frac{39999 + 2398 + 780 - 9977}{40000}$

Step 5

Reduce the expression by cancelling the common factors.

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Step 5.1

Add $39999$ and $2398$ .

$\frac{42397 + 780 - 9977}{40000}$

Step 5.2

Simplify by adding and subtracting.

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Step 5.2.1

Add $42397$ and $780$ .

$\frac{43177 - 9977}{40000}$

Step 5.2.2

Subtract $9977$ from $43177$ .

$\frac{33200}{40000}$

Step 5.3

Cancel the common factor of $33200$ and $40000$ .

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Step 5.3.1

Factor $400$ out of $33200$ .

$\frac{400 (83)}{40000}$

Step 5.3.2

Cancel the common factors.

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Step 5.3.2.1

Factor $400$ out of $40000$ .

$\frac{400 \cdot 83}{400 \cdot 100}$

Step 5.3.2.2

Cancel the common factor.

$\frac{400 \cdot 83}{400 \cdot 100}$

Step 5.3.2.3

Rewrite the expression.

$\frac{83}{100}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{83}{100}$

Decimal Form:

$0.83$