Pre-Algebra Examples

$\frac{1}{3} x - \frac{1}{15} = \frac{1}{3}$

Step 1

Combine $\frac{1}{3}$ and $x$ .

$\frac{x}{3} - \frac{1}{15} = \frac{1}{3}$

Step 2

Move all terms not containing $x$ to the right side of the equation.

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Step 2.1

Add $\frac{1}{15}$ to both sides of the equation.

$\frac{x}{3} = \frac{1}{3} + \frac{1}{15}$

Step 2.2

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{x}{3} = \frac{1}{3} \cdot \frac{5}{5} + \frac{1}{15}$

Step 2.3

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.3.1

Multiply $\frac{1}{3}$ by $\frac{5}{5}$ .

$\frac{x}{3} = \frac{5}{3 \cdot 5} + \frac{1}{15}$

Step 2.3.2

Multiply $3$ by $5$ .

$\frac{x}{3} = \frac{5}{15} + \frac{1}{15}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{x}{3} = \frac{5 + 1}{15}$

Step 2.5

Add $5$ and $1$ .

$\frac{x}{3} = \frac{6}{15}$

Step 2.6

Cancel the common factor of $6$ and $15$ .

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Step 2.6.1

Factor $3$ out of $6$ .

$\frac{x}{3} = \frac{3 (2)}{15}$

Step 2.6.2

Cancel the common factors.

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Step 2.6.2.1

Factor $3$ out of $15$ .

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

Step 2.6.2.2

Cancel the common factor.

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

Step 2.6.2.3

Rewrite the expression.

$\frac{x}{3} = \frac{2}{5}$

Step 3

Multiply both sides of the equation by $3$ .

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

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Cancel the common factor of $3$ .

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Step 4.1.1.1

Cancel the common factor.

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

Step 4.1.1.2

Rewrite the expression.

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

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $3 (\frac{2}{5})$ .

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Step 4.2.1.1

Combine $3$ and $\frac{2}{5}$ .

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

Step 4.2.1.2

Multiply $3$ by $2$ .

$x = \frac{6}{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{6}{5}$

Decimal Form:

$x = 1.2$

Mixed Number Form:

$x = 1 \frac{1}{5}$