Finite Math Examples

$\frac{1}{1000} \cdot (900) + \frac{999}{1000} \cdot (- 2)$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $100$ .

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Step 1.1.1

Factor $100$ out of $1000$ .

$\frac{1}{100 (10)} \cdot 900 + \frac{999}{1000} \cdot (- 2)$

Step 1.1.2

Factor $100$ out of $900$ .

$\frac{1}{100 \cdot 10} \cdot (100 \cdot 9) + \frac{999}{1000} \cdot (- 2)$

Step 1.1.3

Cancel the common factor.

$\frac{1}{100 \cdot 10} \cdot (100 \cdot 9) + \frac{999}{1000} \cdot (- 2)$

Step 1.1.4

Rewrite the expression.

$\frac{1}{10} \cdot 9 + \frac{999}{1000} \cdot (- 2)$

Step 1.2

Combine $\frac{1}{10}$ and $9$ .

$\frac{9}{10} + \frac{999}{1000} \cdot (- 2)$

Step 1.3

Cancel the common factor of $2$ .

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Step 1.3.1

Factor $2$ out of $1000$ .

$\frac{9}{10} + \frac{999}{2 (500)} \cdot - 2$

Step 1.3.2

Factor $2$ out of $- 2$ .

$\frac{9}{10} + \frac{999}{2 \cdot 500} \cdot (2 \cdot - 1)$

Step 1.3.3

Cancel the common factor.

$\frac{9}{10} + \frac{999}{2 \cdot 500} \cdot (2 \cdot - 1)$

Step 1.3.4

Rewrite the expression.

$\frac{9}{10} + \frac{999}{500} \cdot - 1$

Step 1.4

Combine $\frac{999}{500}$ and $- 1$ .

$\frac{9}{10} + \frac{999 \cdot - 1}{500}$

Step 1.5

Multiply $999$ by $- 1$ .

$\frac{9}{10} + \frac{- 999}{500}$

Step 1.6

Move the negative in front of the fraction.

$\frac{9}{10} - \frac{999}{500}$

Step 2

To write $\frac{9}{10}$ as a fraction with a common denominator, multiply by $\frac{50}{50}$ .

$\frac{9}{10} \cdot \frac{50}{50} - \frac{999}{500}$

Step 3

Write each expression with a common denominator of $500$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{9}{10}$ by $\frac{50}{50}$ .

$\frac{9 \cdot 50}{10 \cdot 50} - \frac{999}{500}$

Step 3.2

Multiply $10$ by $50$ .

$\frac{9 \cdot 50}{500} - \frac{999}{500}$

Step 4

Combine the numerators over the common denominator.

$\frac{9 \cdot 50 - 999}{500}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $9$ by $50$ .

$\frac{450 - 999}{500}$

Step 5.2

Subtract $999$ from $450$ .

$\frac{- 549}{500}$

Step 6

Move the negative in front of the fraction.

$- \frac{549}{500}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{549}{500}$

Decimal Form:

$- 1.098$

Mixed Number Form:

$- 1 \frac{49}{500}$