Pre-Algebra Examples

$- \frac{4 v}{5} = 8$

Step 1

Multiply both sides of the equation by $- \frac{5}{4}$ .

$- \frac{5}{4} (- \frac{4 v}{5}) = - \frac{5}{4} \cdot 8$

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 $- \frac{5}{4} (- \frac{4 v}{5})$ .

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Step 2.1.1.1

Cancel the common factor of $5$ .

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Step 2.1.1.1.1

Move the leading negative in $- \frac{5}{4}$ into the numerator.

$\frac{- 5}{4} (- \frac{4 v}{5}) = - \frac{5}{4} \cdot 8$

Step 2.1.1.1.2

Move the leading negative in $- \frac{4 v}{5}$ into the numerator.

$\frac{- 5}{4} \cdot \frac{- 4 v}{5} = - \frac{5}{4} \cdot 8$

Step 2.1.1.1.3

Factor $5$ out of $- 5$ .

$\frac{5 (- 1)}{4} \cdot \frac{- 4 v}{5} = - \frac{5}{4} \cdot 8$

Step 2.1.1.1.4

Cancel the common factor.

$\frac{5 \cdot - 1}{4} \cdot \frac{- 4 v}{5} = - \frac{5}{4} \cdot 8$

Step 2.1.1.1.5

Rewrite the expression.

$\frac{- 1}{4} (- 4 v) = - \frac{5}{4} \cdot 8$

Step 2.1.1.2

Cancel the common factor of $4$ .

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Step 2.1.1.2.1

Factor $4$ out of $- 4 v$ .

$\frac{- 1}{4} (4 (- v)) = - \frac{5}{4} \cdot 8$

Step 2.1.1.2.2

Cancel the common factor.

$\frac{- 1}{4} (4 (- v)) = - \frac{5}{4} \cdot 8$

Step 2.1.1.2.3

Rewrite the expression.

$- - v = - \frac{5}{4} \cdot 8$

Step 2.1.1.3

Multiply.

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Step 2.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 v = - \frac{5}{4} \cdot 8$

Step 2.1.1.3.2

Multiply $v$ by $1$ .

$v = - \frac{5}{4} \cdot 8$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $- \frac{5}{4} \cdot 8$ .

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Step 2.2.1.1

Cancel the common factor of $4$ .

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Step 2.2.1.1.1

Move the leading negative in $- \frac{5}{4}$ into the numerator.

$v = \frac{- 5}{4} \cdot 8$

Step 2.2.1.1.2

Factor $4$ out of $8$ .

$v = \frac{- 5}{4} \cdot (4 (2))$

Step 2.2.1.1.3

Cancel the common factor.

$v = \frac{- 5}{4} \cdot (4 \cdot 2)$

Step 2.2.1.1.4

Rewrite the expression.

$v = - 5 \cdot 2$

Step 2.2.1.2

Multiply $- 5$ by $2$ .

$v = - 10$