Finite Math Examples

$999.25 \cdot \frac{1}{15000} + 299.25 \cdot \frac{2}{15000} + 9.25 \cdot \frac{20}{15000} - 0.75 \cdot \frac{14997}{15000}$

Step 1

Simplify each term.

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Step 1.1

Combine $999.25$ and $\frac{1}{15000}$ .

$\frac{999.25}{15000} + 299.25 \cdot \frac{2}{15000} + 9.25 \cdot \frac{20}{15000} - 0.75 \cdot \frac{14997}{15000}$

Step 1.2

Divide $999.25$ by $15000$ .

$0.06661\overline{6} + 299.25 \cdot \frac{2}{15000} + 9.25 \cdot \frac{20}{15000} - 0.75 \cdot \frac{14997}{15000}$

Step 1.3

Cancel the common factor of $2$ and $15000$ .

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Step 1.3.1

Factor $2$ out of $2$ .

$0.06661\overline{6} + 299.25 \cdot \frac{2 (1)}{15000} + 9.25 \cdot \frac{20}{15000} - 0.75 \cdot \frac{14997}{15000}$

Step 1.3.2

Cancel the common factors.

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Step 1.3.2.1

Factor $2$ out of $15000$ .

$0.06661\overline{6} + 299.25 \cdot \frac{2 \cdot 1}{2 \cdot 7500} + 9.25 \cdot \frac{20}{15000} - 0.75 \cdot \frac{14997}{15000}$

Step 1.3.2.2

Cancel the common factor.

$0.06661\overline{6} + 299.25 \cdot \frac{2 \cdot 1}{2 \cdot 7500} + 9.25 \cdot \frac{20}{15000} - 0.75 \cdot \frac{14997}{15000}$

Step 1.3.2.3

Rewrite the expression.

$0.06661\overline{6} + 299.25 \cdot \frac{1}{7500} + 9.25 \cdot \frac{20}{15000} - 0.75 \cdot \frac{14997}{15000}$

Step 1.4

Combine $299.25$ and $\frac{1}{7500}$ .

$0.06661\overline{6} + \frac{299.25}{7500} + 9.25 \cdot \frac{20}{15000} - 0.75 \cdot \frac{14997}{15000}$

Step 1.5

Divide $299.25$ by $7500$ .

$0.06661\overline{6} + 0.0399 + 9.25 \cdot \frac{20}{15000} - 0.75 \cdot \frac{14997}{15000}$

Step 1.6

Cancel the common factor of $20$ and $15000$ .

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Step 1.6.1

Factor $20$ out of $20$ .

$0.06661\overline{6} + 0.0399 + 9.25 \cdot \frac{20 (1)}{15000} - 0.75 \cdot \frac{14997}{15000}$

Step 1.6.2

Cancel the common factors.

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Step 1.6.2.1

Factor $20$ out of $15000$ .

$0.06661\overline{6} + 0.0399 + 9.25 \cdot \frac{20 \cdot 1}{20 \cdot 750} - 0.75 \cdot \frac{14997}{15000}$

Step 1.6.2.2

Cancel the common factor.

$0.06661\overline{6} + 0.0399 + 9.25 \cdot \frac{20 \cdot 1}{20 \cdot 750} - 0.75 \cdot \frac{14997}{15000}$

Step 1.6.2.3

Rewrite the expression.

$0.06661\overline{6} + 0.0399 + 9.25 \cdot \frac{1}{750} - 0.75 \cdot \frac{14997}{15000}$

Step 1.7

Combine $9.25$ and $\frac{1}{750}$ .

$0.06661\overline{6} + 0.0399 + \frac{9.25}{750} - 0.75 \cdot \frac{14997}{15000}$

Step 1.8

Divide $9.25$ by $750$ .

$0.06661\overline{6} + 0.0399 + 0.012\overline{3} - 0.75 \cdot \frac{14997}{15000}$

Step 1.9

Cancel the common factor of $0.75$ .

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Step 1.9.1

Factor $0.75$ out of $- 0.75$ .

$0.06661\overline{6} + 0.0399 + 0.012\overline{3} + 0.75 (- 1) \cdot \frac{14997}{15000}$

Step 1.9.2

Factor $0.75$ out of $15000$ .

$0.06661\overline{6} + 0.0399 + 0.012\overline{3} + 0.75 \cdot - 1 \cdot \frac{14997}{0.75 \cdot 20000}$

Step 1.9.3

Cancel the common factor.

$0.06661\overline{6} + 0.0399 + 0.012\overline{3} + 0.75 \cdot - 1 \cdot \frac{14997}{0.75 \cdot 20000}$

Step 1.9.4

Rewrite the expression.

$0.06661\overline{6} + 0.0399 + 0.012\overline{3} - 1 \cdot \frac{14997}{20000}$

Step 1.10

Rewrite $- 1 (\frac{14997}{20000})$ as $- (\frac{14997}{20000})$ .

$0.06661\overline{6} + 0.0399 + 0.012\overline{3} - \frac{14997}{20000}$

Step 2

Find the common denominator.

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Step 2.1

Write $0.06661\overline{6}$ as a fraction with denominator $1$ .

$\frac{0.06661\overline{6}}{1} + 0.0399 + 0.012\overline{3} - \frac{14997}{20000}$

Step 2.2

Multiply $\frac{0.06661\overline{6}}{1}$ by $\frac{20000}{20000}$ .

$\frac{0.06661\overline{6}}{1} \cdot \frac{20000}{20000} + 0.0399 + 0.012\overline{3} - \frac{14997}{20000}$

Step 2.3

Multiply $\frac{0.06661\overline{6}}{1}$ by $\frac{20000}{20000}$ .

$\frac{0.06661\overline{6} \cdot 20000}{20000} + 0.0399 + 0.012\overline{3} - \frac{14997}{20000}$

Step 2.4

Write $0.0399$ as a fraction with denominator $1$ .

$\frac{0.06661\overline{6} \cdot 20000}{20000} + \frac{0.0399}{1} + 0.012\overline{3} - \frac{14997}{20000}$

Step 2.5

Multiply $\frac{0.0399}{1}$ by $\frac{20000}{20000}$ .

$\frac{0.06661\overline{6} \cdot 20000}{20000} + \frac{0.0399}{1} \cdot \frac{20000}{20000} + 0.012\overline{3} - \frac{14997}{20000}$

Step 2.6

Multiply $\frac{0.0399}{1}$ by $\frac{20000}{20000}$ .

$\frac{0.06661\overline{6} \cdot 20000}{20000} + \frac{0.0399 \cdot 20000}{20000} + 0.012\overline{3} - \frac{14997}{20000}$

Step 2.7

Write $0.012\overline{3}$ as a fraction with denominator $1$ .

$\frac{0.06661\overline{6} \cdot 20000}{20000} + \frac{0.0399 \cdot 20000}{20000} + \frac{0.012\overline{3}}{1} - \frac{14997}{20000}$

Step 2.8

Multiply $\frac{0.012\overline{3}}{1}$ by $\frac{20000}{20000}$ .

$\frac{0.06661\overline{6} \cdot 20000}{20000} + \frac{0.0399 \cdot 20000}{20000} + \frac{0.012\overline{3}}{1} \cdot \frac{20000}{20000} - \frac{14997}{20000}$

Step 2.9

Multiply $\frac{0.012\overline{3}}{1}$ by $\frac{20000}{20000}$ .

$\frac{0.06661\overline{6} \cdot 20000}{20000} + \frac{0.0399 \cdot 20000}{20000} + \frac{0.012\overline{3} \cdot 20000}{20000} - \frac{14997}{20000}$

Step 3

Combine the numerators over the common denominator.

$\frac{0.06661\overline{6} \cdot 20000 + 0.0399 \cdot 20000 + 0.012\overline{3} \cdot 20000 - 14997}{20000}$

Step 4

Simplify each term.

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Step 4.1

Multiply $0.06661\overline{6}$ by $20000$ .

$\frac{1332.\overline{3} + 0.0399 \cdot 20000 + 0.012\overline{3} \cdot 20000 - 14997}{20000}$

Step 4.2

Multiply $0.0399$ by $20000$ .

$\frac{1332.\overline{3} + 798 + 0.012\overline{3} \cdot 20000 - 14997}{20000}$

Step 4.3

Multiply $0.012\overline{3}$ by $20000$ .

$\frac{1332.\overline{3} + 798 + 246.\overline{6} - 14997}{20000}$

Step 5

Reduce the expression by cancelling the common factors.

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Step 5.1

Add $1332.\overline{3}$ and $798$ .

$\frac{2130.\overline{3} + 246.\overline{6} - 14997}{20000}$

Step 5.2

Simplify by adding and subtracting.

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Step 5.2.1

Add $2130.\overline{3}$ and $246.\overline{6}$ .

$\frac{2377 - 14997}{20000}$

Step 5.2.2

Subtract $14997$ from $2377$ .

$\frac{- 12620}{20000}$

Step 5.3

Cancel the common factor of $- 12620$ and $20000$ .

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Step 5.3.1

Factor $20$ out of $- 12620$ .

$\frac{20 (- 631)}{20000}$

Step 5.3.2

Cancel the common factors.

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Step 5.3.2.1

Factor $20$ out of $20000$ .

$\frac{20 \cdot - 631}{20 \cdot 1000}$

Step 5.3.2.2

Cancel the common factor.

$\frac{20 \cdot - 631}{20 \cdot 1000}$

Step 5.3.2.3

Rewrite the expression.

$\frac{- 631}{1000}$

Step 5.4

Move the negative in front of the fraction.

$- \frac{631}{1000}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \frac{631}{1000}$

Decimal Form:

$- 0.631$