Basic Math Examples

$- 415 = - 500 a - b$

Step 1

Rewrite the equation as $- 500 a - b = - 415$ .

$- 500 a - b = - 415$

Step 2

Add $b$ to both sides of the equation.

$- 500 a = - 415 + b$

Step 3

Divide each term in $- 500 a = - 415 + b$ by $- 500$ and simplify.

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Step 3.1

Divide each term in $- 500 a = - 415 + b$ by $- 500$ .

$\frac{- 500 a}{- 500} = \frac{- 415}{- 500} + \frac{b}{- 500}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 500$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{- 500 a}{- 500} = \frac{- 415}{- 500} + \frac{b}{- 500}$

Step 3.2.1.2

Divide $a$ by $1$ .

$a = \frac{- 415}{- 500} + \frac{b}{- 500}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify each term.

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Step 3.3.1.1

Cancel the common factor of $- 415$ and $- 500$ .

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Step 3.3.1.1.1

Factor $- 5$ out of $- 415$ .

$a = \frac{- 5 (83)}{- 500} + \frac{b}{- 500}$

Step 3.3.1.1.2

Cancel the common factors.

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Step 3.3.1.1.2.1

Factor $- 5$ out of $- 500$ .

$a = \frac{- 5 \cdot 83}{- 5 \cdot 100} + \frac{b}{- 500}$

Step 3.3.1.1.2.2

Cancel the common factor.

$a = \frac{- 5 \cdot 83}{- 5 \cdot 100} + \frac{b}{- 500}$

Step 3.3.1.1.2.3

Rewrite the expression.

$a = \frac{83}{100} + \frac{b}{- 500}$

Step 3.3.1.2

Move the negative in front of the fraction.

$a = \frac{83}{100} - \frac{b}{500}$