Finite Math Examples

$\frac{1}{500} \cdot (397 - x) + \frac{2}{500} \cdot (272 - x) + \frac{5}{500} \cdot (97 - x) + \frac{492}{500} \cdot (- x)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$\frac{1}{500} \cdot 397 + \frac{1}{500} (- x) + \frac{2}{500} \cdot (272 - x) + \frac{5}{500} \cdot (97 - x) + \frac{492}{500} \cdot (- x)$

Step 1.2

Combine $\frac{1}{500}$ and $397$ .

$\frac{397}{500} + \frac{1}{500} (- x) + \frac{2}{500} \cdot (272 - x) + \frac{5}{500} \cdot (97 - x) + \frac{492}{500} \cdot (- x)$

Step 1.3

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

$\frac{397}{500} - \frac{x}{500} + \frac{2}{500} \cdot (272 - x) + \frac{5}{500} \cdot (97 - x) + \frac{492}{500} \cdot (- x)$

Step 1.4

Cancel the common factor of $2$ and $500$ .

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Step 1.4.1

Factor $2$ out of $2$ .

$\frac{397}{500} - \frac{x}{500} + \frac{2 (1)}{500} \cdot (272 - x) + \frac{5}{500} \cdot (97 - x) + \frac{492}{500} \cdot (- x)$

Step 1.4.2

Cancel the common factors.

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Step 1.4.2.1

Factor $2$ out of $500$ .

$\frac{397}{500} - \frac{x}{500} + \frac{2 \cdot 1}{2 \cdot 250} \cdot (272 - x) + \frac{5}{500} \cdot (97 - x) + \frac{492}{500} \cdot (- x)$

Step 1.4.2.2

Cancel the common factor.

$\frac{397}{500} - \frac{x}{500} + \frac{2 \cdot 1}{2 \cdot 250} \cdot (272 - x) + \frac{5}{500} \cdot (97 - x) + \frac{492}{500} \cdot (- x)$

Step 1.4.2.3

Rewrite the expression.

$\frac{397}{500} - \frac{x}{500} + \frac{1}{250} \cdot (272 - x) + \frac{5}{500} \cdot (97 - x) + \frac{492}{500} \cdot (- x)$

Step 1.5

Apply the distributive property.

$\frac{397}{500} - \frac{x}{500} + \frac{1}{250} \cdot 272 + \frac{1}{250} (- x) + \frac{5}{500} \cdot (97 - x) + \frac{492}{500} \cdot (- x)$

Step 1.6

Cancel the common factor of $2$ .

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Step 1.6.1

Factor $2$ out of $250$ .

$\frac{397}{500} - \frac{x}{500} + \frac{1}{2 (125)} \cdot 272 + \frac{1}{250} (- x) + \frac{5}{500} \cdot (97 - x) + \frac{492}{500} \cdot (- x)$

Step 1.6.2

Factor $2$ out of $272$ .

$\frac{397}{500} - \frac{x}{500} + \frac{1}{2 \cdot 125} \cdot (2 \cdot 136) + \frac{1}{250} (- x) + \frac{5}{500} \cdot (97 - x) + \frac{492}{500} \cdot (- x)$

Step 1.6.3

Cancel the common factor.

$\frac{397}{500} - \frac{x}{500} + \frac{1}{2 \cdot 125} \cdot (2 \cdot 136) + \frac{1}{250} (- x) + \frac{5}{500} \cdot (97 - x) + \frac{492}{500} \cdot (- x)$

Step 1.6.4

Rewrite the expression.

$\frac{397}{500} - \frac{x}{500} + \frac{1}{125} \cdot 136 + \frac{1}{250} (- x) + \frac{5}{500} \cdot (97 - x) + \frac{492}{500} \cdot (- x)$

Step 1.7

Combine $\frac{1}{125}$ and $136$ .

$\frac{397}{500} - \frac{x}{500} + \frac{136}{125} + \frac{1}{250} (- x) + \frac{5}{500} \cdot (97 - x) + \frac{492}{500} \cdot (- x)$

Step 1.8

Combine $\frac{1}{250}$ and $x$ .

$\frac{397}{500} - \frac{x}{500} + \frac{136}{125} - \frac{x}{250} + \frac{5}{500} \cdot (97 - x) + \frac{492}{500} \cdot (- x)$

Step 1.9

Cancel the common factor of $5$ and $500$ .

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Step 1.9.1

Factor $5$ out of $5$ .

$\frac{397}{500} - \frac{x}{500} + \frac{136}{125} - \frac{x}{250} + \frac{5 (1)}{500} \cdot (97 - x) + \frac{492}{500} \cdot (- x)$

Step 1.9.2

Cancel the common factors.

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Step 1.9.2.1

Factor $5$ out of $500$ .

$\frac{397}{500} - \frac{x}{500} + \frac{136}{125} - \frac{x}{250} + \frac{5 \cdot 1}{5 \cdot 100} \cdot (97 - x) + \frac{492}{500} \cdot (- x)$

Step 1.9.2.2

Cancel the common factor.

$\frac{397}{500} - \frac{x}{500} + \frac{136}{125} - \frac{x}{250} + \frac{5 \cdot 1}{5 \cdot 100} \cdot (97 - x) + \frac{492}{500} \cdot (- x)$

Step 1.9.2.3

Rewrite the expression.

$\frac{397}{500} - \frac{x}{500} + \frac{136}{125} - \frac{x}{250} + \frac{1}{100} \cdot (97 - x) + \frac{492}{500} \cdot (- x)$

Step 1.10

Apply the distributive property.

$\frac{397}{500} - \frac{x}{500} + \frac{136}{125} - \frac{x}{250} + \frac{1}{100} \cdot 97 + \frac{1}{100} (- x) + \frac{492}{500} \cdot (- x)$

Step 1.11

Combine $\frac{1}{100}$ and $97$ .

$\frac{397}{500} - \frac{x}{500} + \frac{136}{125} - \frac{x}{250} + \frac{97}{100} + \frac{1}{100} (- x) + \frac{492}{500} \cdot (- x)$

Step 1.12

Combine $\frac{1}{100}$ and $x$ .

$\frac{397}{500} - \frac{x}{500} + \frac{136}{125} - \frac{x}{250} + \frac{97}{100} - \frac{x}{100} + \frac{492}{500} \cdot (- x)$

Step 1.13

Cancel the common factor of $492$ and $500$ .

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Step 1.13.1

Factor $4$ out of $492$ .

$\frac{397}{500} - \frac{x}{500} + \frac{136}{125} - \frac{x}{250} + \frac{97}{100} - \frac{x}{100} + \frac{4 (123)}{500} \cdot (- x)$

Step 1.13.2

Cancel the common factors.

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Step 1.13.2.1

Factor $4$ out of $500$ .

$\frac{397}{500} - \frac{x}{500} + \frac{136}{125} - \frac{x}{250} + \frac{97}{100} - \frac{x}{100} + \frac{4 \cdot 123}{4 \cdot 125} \cdot (- x)$

Step 1.13.2.2

Cancel the common factor.

$\frac{397}{500} - \frac{x}{500} + \frac{136}{125} - \frac{x}{250} + \frac{97}{100} - \frac{x}{100} + \frac{4 \cdot 123}{4 \cdot 125} \cdot (- x)$

Step 1.13.2.3

Rewrite the expression.

$\frac{397}{500} - \frac{x}{500} + \frac{136}{125} - \frac{x}{250} + \frac{97}{100} - \frac{x}{100} + \frac{123}{125} \cdot (- x)$

Step 1.14

Combine $\frac{123}{125}$ and $x$ .

$\frac{397}{500} - \frac{x}{500} + \frac{136}{125} - \frac{x}{250} + \frac{97}{100} - \frac{x}{100} - \frac{123 x}{125}$

Step 2

To write $\frac{136}{125}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- \frac{x}{500} + \frac{397}{500} + \frac{136}{125} \cdot \frac{4}{4} - \frac{x}{250} + \frac{97}{100} - \frac{x}{100} - \frac{123 x}{125}$

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 $\frac{136}{125}$ by $\frac{4}{4}$ .

$- \frac{x}{500} + \frac{397}{500} + \frac{136 \cdot 4}{125 \cdot 4} - \frac{x}{250} + \frac{97}{100} - \frac{x}{100} - \frac{123 x}{125}$

Step 3.2

Multiply $125$ by $4$ .

$- \frac{x}{500} + \frac{397}{500} + \frac{136 \cdot 4}{500} - \frac{x}{250} + \frac{97}{100} - \frac{x}{100} - \frac{123 x}{125}$

Step 4

Combine the numerators over the common denominator.

$- \frac{x}{500} + \frac{397 + 136 \cdot 4}{500} - \frac{x}{250} + \frac{97}{100} - \frac{x}{100} - \frac{123 x}{125}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $136$ by $4$ .

$- \frac{x}{500} + \frac{397 + 544}{500} - \frac{x}{250} + \frac{97}{100} - \frac{x}{100} - \frac{123 x}{125}$

Step 5.2

Add $397$ and $544$ .

$- \frac{x}{500} + \frac{941}{500} - \frac{x}{250} + \frac{97}{100} - \frac{x}{100} - \frac{123 x}{125}$

Step 6

To write $- \frac{x}{250}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{x}{500} - \frac{x}{250} \cdot \frac{2}{2} + \frac{941}{500} + \frac{97}{100} - \frac{x}{100} - \frac{123 x}{125}$

Step 7

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

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Step 7.1

Multiply $\frac{x}{250}$ by $\frac{2}{2}$ .

$- \frac{x}{500} - \frac{x \cdot 2}{250 \cdot 2} + \frac{941}{500} + \frac{97}{100} - \frac{x}{100} - \frac{123 x}{125}$

Step 7.2

Multiply $250$ by $2$ .

$- \frac{x}{500} - \frac{x \cdot 2}{500} + \frac{941}{500} + \frac{97}{100} - \frac{x}{100} - \frac{123 x}{125}$

Step 8

Simplify terms.

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Step 8.1

Combine the numerators over the common denominator.

$\frac{- x - x \cdot 2}{500} + \frac{941}{500} + \frac{97}{100} - \frac{x}{100} - \frac{123 x}{125}$

Step 8.2

Combine the numerators over the common denominator.

$\frac{- x - x \cdot 2 + 941}{500} + \frac{97}{100} + \frac{- x}{100} + \frac{- 123 x}{125}$

Step 8.3

Multiply $2$ by $- 1$ .

$\frac{- x - 2 x + 941}{500} + \frac{97}{100} + \frac{- x}{100} + \frac{- 123 x}{125}$

Step 8.4

Subtract $2 x$ from $- x$ .

$\frac{- 3 x + 941}{500} + \frac{97}{100} + \frac{- x}{100} + \frac{- 123 x}{125}$

Step 9

Simplify each term.

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Step 9.1

Move the negative in front of the fraction.

$\frac{- 3 x + 941}{500} + \frac{97}{100} - \frac{x}{100} + \frac{- 123 x}{125}$

Step 9.2

Move the negative in front of the fraction.

$\frac{- 3 x + 941}{500} + \frac{97}{100} - \frac{x}{100} - \frac{123 x}{125}$

Step 10

To write $\frac{97}{100}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{- 3 x + 941}{500} + \frac{97}{100} \cdot \frac{5}{5} - \frac{x}{100} - \frac{123 x}{125}$

Step 11

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

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Step 11.1

Multiply $\frac{97}{100}$ by $\frac{5}{5}$ .

$\frac{- 3 x + 941}{500} + \frac{97 \cdot 5}{100 \cdot 5} - \frac{x}{100} - \frac{123 x}{125}$

Step 11.2

Multiply $100$ by $5$ .

$\frac{- 3 x + 941}{500} + \frac{97 \cdot 5}{500} - \frac{x}{100} - \frac{123 x}{125}$

Step 12

Combine the numerators over the common denominator.

$\frac{- 3 x + 941 + 97 \cdot 5}{500} - \frac{x}{100} - \frac{123 x}{125}$

Step 13

Simplify the expression.

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Step 13.1

Multiply $97$ by $5$ .

$\frac{- 3 x + 941 + 485}{500} - \frac{x}{100} - \frac{123 x}{125}$

Step 13.2

Add $941$ and $485$ .

$\frac{- 3 x + 1426}{500} - \frac{x}{100} - \frac{123 x}{125}$

Step 14

Find the common denominator.

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Step 14.1

Multiply $\frac{x}{100}$ by $\frac{5}{5}$ .

$\frac{- 3 x + 1426}{500} - (\frac{x}{100} \cdot \frac{5}{5}) - \frac{123 x}{125}$

Step 14.2

Multiply $\frac{x}{100}$ by $\frac{5}{5}$ .

$\frac{- 3 x + 1426}{500} - \frac{x \cdot 5}{100 \cdot 5} - \frac{123 x}{125}$

Step 14.3

Multiply $\frac{123 x}{125}$ by $\frac{4}{4}$ .

$\frac{- 3 x + 1426}{500} - \frac{x \cdot 5}{100 \cdot 5} - (\frac{123 x}{125} \cdot \frac{4}{4})$

Step 14.4

Multiply $\frac{123 x}{125}$ by $\frac{4}{4}$ .

$\frac{- 3 x + 1426}{500} - \frac{x \cdot 5}{100 \cdot 5} - \frac{123 x \cdot 4}{125 \cdot 4}$

Step 14.5

Reorder the factors of $100 \cdot 5$ .

$\frac{- 3 x + 1426}{500} - \frac{x \cdot 5}{5 \cdot 100} - \frac{123 x \cdot 4}{125 \cdot 4}$

Step 14.6

Multiply $5$ by $100$ .

$\frac{- 3 x + 1426}{500} - \frac{x \cdot 5}{500} - \frac{123 x \cdot 4}{125 \cdot 4}$

Step 14.7

Reorder the factors of $125 \cdot 4$ .

$\frac{- 3 x + 1426}{500} - \frac{x \cdot 5}{500} - \frac{123 x \cdot 4}{4 \cdot 125}$

Step 14.8

Multiply $4$ by $125$ .

$\frac{- 3 x + 1426}{500} - \frac{x \cdot 5}{500} - \frac{123 x \cdot 4}{500}$

Step 15

Combine the numerators over the common denominator.

$\frac{- 3 x + 1426 - x \cdot 5 - 123 x \cdot 4}{500}$

Step 16

Simplify each term.

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Step 16.1

Multiply $5$ by $- 1$ .

$\frac{- 3 x + 1426 - 5 x - 123 x \cdot 4}{500}$

Step 16.2

Multiply $4$ by $- 123$ .

$\frac{- 3 x + 1426 - 5 x - 492 x}{500}$

Step 17

Simplify terms.

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Step 17.1

Subtract $5 x$ from $- 3 x$ .

$\frac{- 8 x + 1426 - 492 x}{500}$

Step 17.2

Subtract $492 x$ from $- 8 x$ .

$\frac{- 500 x + 1426}{500}$

Step 17.3

Cancel the common factor of $- 500 x + 1426$ and $500$ .

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Step 17.3.1

Factor $2$ out of $- 500 x$ .

$\frac{2 (- 250 x) + 1426}{500}$

Step 17.3.2

Factor $2$ out of $1426$ .

$\frac{2 (- 250 x) + 2 (713)}{500}$

Step 17.3.3

Factor $2$ out of $2 (- 250 x) + 2 (713)$ .

$\frac{2 (- 250 x + 713)}{500}$

Step 17.3.4

Cancel the common factors.

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Step 17.3.4.1

Factor $2$ out of $500$ .

$\frac{2 (- 250 x + 713)}{2 (250)}$

Step 17.3.4.2

Cancel the common factor.

$\frac{2 (- 250 x + 713)}{2 \cdot 250}$

Step 17.3.4.3

Rewrite the expression.

$\frac{- 250 x + 713}{250}$

Step 17.4

Factor $- 1$ out of $- 250 x$ .

$\frac{- (250 x) + 713}{250}$

Step 17.5

Rewrite $713$ as $- 1 (- 713)$ .

$\frac{- (250 x) - 1 (- 713)}{250}$

Step 17.6

Factor $- 1$ out of $- (250 x) - 1 (- 713)$ .

$\frac{- (250 x - 713)}{250}$

Step 17.7

Simplify the expression.

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Step 17.7.1

Rewrite $- (250 x - 713)$ as $- 1 (250 x - 713)$ .

$\frac{- 1 (250 x - 713)}{250}$

Step 17.7.2

Move the negative in front of the fraction.

$- \frac{250 x - 713}{250}$