Pre-Algebra Examples

$\frac{- 5 a}{2} = 75$

Step 1

Multiply both sides of the equation by $\frac{2}{- 5}$ .

$\frac{2}{- 5} \cdot \frac{- 5 a}{2} = \frac{2}{- 5} \cdot 75$

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{2}{- 5} \cdot \frac{- 5 a}{2}$ .

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Step 2.1.1.1

Cancel the common factor of $2$ .

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Step 2.1.1.1.1

Cancel the common factor.

$\frac{2}{- 5} \cdot \frac{- 5 a}{2} = \frac{2}{- 5} \cdot 75$

Step 2.1.1.1.2

Rewrite the expression.

$\frac{1}{- 5} (- 5 a) = \frac{2}{- 5} \cdot 75$

Step 2.1.1.2

Cancel the common factor of $5$ .

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Step 2.1.1.2.1

Factor $5$ out of $- 5$ .

$\frac{1}{5 (- 1)} (- 5 a) = \frac{2}{- 5} \cdot 75$

Step 2.1.1.2.2

Factor $5$ out of $- 5 a$ .

$\frac{1}{5 (- 1)} (5 (- a)) = \frac{2}{- 5} \cdot 75$

Step 2.1.1.2.3

Cancel the common factor.

$\frac{1}{5 \cdot - 1} (5 (- a)) = \frac{2}{- 5} \cdot 75$

Step 2.1.1.2.4

Rewrite the expression.

$\frac{1}{- 1} (- a) = \frac{2}{- 5} \cdot 75$

Step 2.1.1.3

Combine $\frac{1}{- 1}$ and $a$ .

$- \frac{a}{- 1} = \frac{2}{- 5} \cdot 75$

Step 2.1.1.4

Simplify the expression.

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Step 2.1.1.4.1

Move the negative one from the denominator of $\frac{a}{- 1}$ .

$- (- 1 \cdot a) = \frac{2}{- 5} \cdot 75$

Step 2.1.1.4.2

Rewrite $- 1 \cdot a$ as $- a$ .

$- - a = \frac{2}{- 5} \cdot 75$

Step 2.1.1.5

Multiply $- - a$ .

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Step 2.1.1.5.1

Multiply $- 1$ by $- 1$ .

$1 a = \frac{2}{- 5} \cdot 75$

Step 2.1.1.5.2

Multiply $a$ by $1$ .

$a = \frac{2}{- 5} \cdot 75$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{2}{- 5} \cdot 75$ .

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Step 2.2.1.1

Cancel the common factor of $5$ .

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Step 2.2.1.1.1

Factor $5$ out of $- 5$ .

$a = \frac{2}{5 (- 1)} \cdot 75$

Step 2.2.1.1.2

Factor $5$ out of $75$ .

$a = \frac{2}{5 \cdot - 1} \cdot (5 \cdot 15)$

Step 2.2.1.1.3

Cancel the common factor.

$a = \frac{2}{5 \cdot - 1} \cdot (5 \cdot 15)$

Step 2.2.1.1.4

Rewrite the expression.

$a = \frac{2}{- 1} \cdot 15$

Step 2.2.1.2

Combine $\frac{2}{- 1}$ and $15$ .

$a = \frac{2 \cdot 15}{- 1}$

Step 2.2.1.3

Simplify the expression.

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Step 2.2.1.3.1

Multiply $2$ by $15$ .

$a = \frac{30}{- 1}$

Step 2.2.1.3.2

Divide $30$ by $- 1$ .

$a = - 30$