Pre-Algebra Examples

$\frac{2}{5} x = - \frac{8}{15}$

Step 1

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

$\frac{5}{2} (\frac{2}{5} x) = \frac{5}{2} (- \frac{8}{15})$

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 $\frac{5}{2} (\frac{2}{5} x)$ .

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Step 2.1.1.1

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

$\frac{5}{2} \cdot \frac{2 x}{5} = \frac{5}{2} (- \frac{8}{15})$

Step 2.1.1.2

Cancel the common factor of $5$ .

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Step 2.1.1.2.1

Cancel the common factor.

$\frac{5}{2} \cdot \frac{2 x}{5} = \frac{5}{2} (- \frac{8}{15})$

Step 2.1.1.2.2

Rewrite the expression.

$\frac{1}{2} (2 x) = \frac{5}{2} (- \frac{8}{15})$

Step 2.1.1.3

Cancel the common factor of $2$ .

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Step 2.1.1.3.1

Factor $2$ out of $2 x$ .

$\frac{1}{2} (2 (x)) = \frac{5}{2} (- \frac{8}{15})$

Step 2.1.1.3.2

Cancel the common factor.

$\frac{1}{2} (2 x) = \frac{5}{2} (- \frac{8}{15})$

Step 2.1.1.3.3

Rewrite the expression.

$x = \frac{5}{2} (- \frac{8}{15})$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{5}{2} (- \frac{8}{15})$ .

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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

Move the leading negative in $- \frac{8}{15}$ into the numerator.

$x = \frac{5}{2} \cdot \frac{- 8}{15}$

Step 2.2.1.1.2

Factor $5$ out of $15$ .

$x = \frac{5}{2} \cdot \frac{- 8}{5 (3)}$

Step 2.2.1.1.3

Cancel the common factor.

$x = \frac{5}{2} \cdot \frac{- 8}{5 \cdot 3}$

Step 2.2.1.1.4

Rewrite the expression.

$x = \frac{1}{2} \cdot \frac{- 8}{3}$

Step 2.2.1.2

Cancel the common factor of $2$ .

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Step 2.2.1.2.1

Factor $2$ out of $- 8$ .

$x = \frac{1}{2} \cdot \frac{2 (- 4)}{3}$

Step 2.2.1.2.2

Cancel the common factor.

$x = \frac{1}{2} \cdot \frac{2 \cdot - 4}{3}$

Step 2.2.1.2.3

Rewrite the expression.

$x = \frac{- 4}{3}$

Step 2.2.1.3

Move the negative in front of the fraction.

$x = - \frac{4}{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{4}{3}$

Decimal Form:

$x = - 1.\overline{3}$

Mixed Number Form:

$x = - 1 \frac{1}{3}$