Pre-Algebra Examples

$\frac{5 n}{6} = - \frac{2}{3}$

Step 1

Multiply both sides of the equation by $\frac{6}{5}$ .

$\frac{6}{5} \cdot \frac{5 n}{6} = \frac{6}{5} (- \frac{2}{3})$

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 $\frac{6}{5} \cdot \frac{5 n}{6}$ .

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Step 2.1.1.1

Cancel the common factor of $6$ .

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Step 2.1.1.1.1

Cancel the common factor.

$\frac{6}{5} \cdot \frac{5 n}{6} = \frac{6}{5} (- \frac{2}{3})$

Step 2.1.1.1.2

Rewrite the expression.

$\frac{1}{5} (5 n) = \frac{6}{5} (- \frac{2}{3})$

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 $5 n$ .

$\frac{1}{5} (5 (n)) = \frac{6}{5} (- \frac{2}{3})$

Step 2.1.1.2.2

Cancel the common factor.

$\frac{1}{5} (5 n) = \frac{6}{5} (- \frac{2}{3})$

Step 2.1.1.2.3

Rewrite the expression.

$n = \frac{6}{5} (- \frac{2}{3})$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{6}{5} (- \frac{2}{3})$ .

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Step 2.2.1.1

Cancel the common factor of $3$ .

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Step 2.2.1.1.1

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$n = \frac{6}{5} \cdot \frac{- 2}{3}$

Step 2.2.1.1.2

Factor $3$ out of $6$ .

$n = \frac{3 (2)}{5} \cdot \frac{- 2}{3}$

Step 2.2.1.1.3

Cancel the common factor.

$n = \frac{3 \cdot 2}{5} \cdot \frac{- 2}{3}$

Step 2.2.1.1.4

Rewrite the expression.

$n = \frac{2}{5} \cdot - 2$

Step 2.2.1.2

Combine $\frac{2}{5}$ and $- 2$ .

$n = \frac{2 \cdot - 2}{5}$

Step 2.2.1.3

Simplify the expression.

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Step 2.2.1.3.1

Multiply $2$ by $- 2$ .

$n = \frac{- 4}{5}$

Step 2.2.1.3.2

Move the negative in front of the fraction.

$n = - \frac{4}{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$n = - \frac{4}{5}$

Decimal Form:

$n = - 0.8$