Pre-Algebra Examples

$\frac{5 x}{6} - \frac{x}{3} = \frac{1}{6}$

Step 1

Simplify $\frac{5 x}{6} - \frac{x}{3}$ .

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Step 1.1

To write $- \frac{x}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{5 x}{6} - \frac{x}{3} \cdot \frac{2}{2} = \frac{1}{6}$

Step 1.2

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.2.1

Multiply $\frac{x}{3}$ by $\frac{2}{2}$ .

$\frac{5 x}{6} - \frac{x \cdot 2}{3 \cdot 2} = \frac{1}{6}$

Step 1.2.2

Multiply $3$ by $2$ .

$\frac{5 x}{6} - \frac{x \cdot 2}{6} = \frac{1}{6}$

Step 1.3

Combine the numerators over the common denominator.

$\frac{5 x - x \cdot 2}{6} = \frac{1}{6}$

Step 1.4

Simplify the numerator.

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Step 1.4.1

Factor $x$ out of $5 x - x \cdot 2$ .

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Step 1.4.1.1

Factor $x$ out of $5 x$ .

$\frac{x \cdot 5 - x \cdot 2}{6} = \frac{1}{6}$

Step 1.4.1.2

Factor $x$ out of $- x \cdot 2$ .

$\frac{x \cdot 5 + x (- 1 \cdot 2)}{6} = \frac{1}{6}$

Step 1.4.1.3

Factor $x$ out of $x \cdot 5 + x (- 1 \cdot 2)$ .

$\frac{x (5 - 1 \cdot 2)}{6} = \frac{1}{6}$

Step 1.4.2

Multiply $- 1$ by $2$ .

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

Step 1.4.3

Subtract $2$ from $5$ .

$\frac{x \cdot 3}{6} = \frac{1}{6}$

Step 1.5

Cancel the common factor of $3$ and $6$ .

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Step 1.5.1

Factor $3$ out of $x \cdot 3$ .

$\frac{3 \cdot x}{6} = \frac{1}{6}$

Step 1.5.2

Cancel the common factors.

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Step 1.5.2.1

Factor $3$ out of $6$ .

$\frac{3 \cdot x}{3 \cdot 2} = \frac{1}{6}$

Step 1.5.2.2

Cancel the common factor.

$\frac{3 \cdot x}{3 \cdot 2} = \frac{1}{6}$

Step 1.5.2.3

Rewrite the expression.

$\frac{x}{2} = \frac{1}{6}$

Step 2

Multiply both sides of the equation by $2$ .

$2 \frac{x}{2} = 2 (\frac{1}{6})$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $2$ .

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Step 3.1.1.1

Cancel the common factor.

$2 \frac{x}{2} = 2 (\frac{1}{6})$

Step 3.1.1.2

Rewrite the expression.

$x = 2 (\frac{1}{6})$

Step 3.2

Simplify the right side.

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Step 3.2.1

Cancel the common factor of $2$ .

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Step 3.2.1.1

Factor $2$ out of $6$ .

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

Step 3.2.1.2

Cancel the common factor.

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

Step 3.2.1.3

Rewrite the expression.

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 0.\overline{3}$