Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

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

Step 1.2

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

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

Step 1.3

Multiply $\frac{1}{3} (- \frac{1}{3})$ .

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Step 1.3.1

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

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

Step 1.3.2

Multiply $3$ by $3$ .

$\frac{x}{3} - \frac{1}{9} - \frac{1}{2} \cdot (\frac{2}{3} x - \frac{1}{2})$

Step 1.4

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

$\frac{x}{3} - \frac{1}{9} - \frac{1}{2} \cdot (\frac{2 x}{3} - \frac{1}{2})$

Step 1.5

Apply the distributive property.

$\frac{x}{3} - \frac{1}{9} - \frac{1}{2} \cdot \frac{2 x}{3} - \frac{1}{2} (- \frac{1}{2})$

Step 1.6

Cancel the common factor of $2$ .

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Step 1.6.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$\frac{x}{3} - \frac{1}{9} + \frac{- 1}{2} \cdot \frac{2 x}{3} - \frac{1}{2} (- \frac{1}{2})$

Step 1.6.2

Factor $2$ out of $2 x$ .

$\frac{x}{3} - \frac{1}{9} + \frac{- 1}{2} \cdot \frac{2 (x)}{3} - \frac{1}{2} (- \frac{1}{2})$

Step 1.6.3

Cancel the common factor.

$\frac{x}{3} - \frac{1}{9} + \frac{- 1}{2} \cdot \frac{2 x}{3} - \frac{1}{2} (- \frac{1}{2})$

Step 1.6.4

Rewrite the expression.

$\frac{x}{3} - \frac{1}{9} - 1 \frac{x}{3} - \frac{1}{2} (- \frac{1}{2})$

Step 1.7

Multiply $- \frac{1}{2} (- \frac{1}{2})$ .

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Step 1.7.1

Multiply $- 1$ by $- 1$ .

$\frac{x}{3} - \frac{1}{9} - 1 \frac{x}{3} + 1 (\frac{1}{2}) \frac{1}{2}$

Step 1.7.2

Multiply $\frac{1}{2}$ by $1$ .

$\frac{x}{3} - \frac{1}{9} - 1 \frac{x}{3} + \frac{1}{2} \cdot \frac{1}{2}$

Step 1.7.3

Multiply $\frac{1}{2}$ by $\frac{1}{2}$ .

$\frac{x}{3} - \frac{1}{9} - 1 \frac{x}{3} + \frac{1}{2 \cdot 2}$

Step 1.7.4

Multiply $2$ by $2$ .

$\frac{x}{3} - \frac{1}{9} - 1 \frac{x}{3} + \frac{1}{4}$

Step 1.8

Rewrite $- 1 \frac{x}{3}$ as $- \frac{x}{3}$ .

$\frac{x}{3} - \frac{1}{9} - \frac{x}{3} + \frac{1}{4}$

Step 2

Combine the opposite terms in $\frac{x}{3} - \frac{1}{9} - \frac{x}{3} + \frac{1}{4}$ .

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Step 2.1

Subtract $\frac{x}{3}$ from $\frac{x}{3}$ .

$0 - \frac{1}{9} + \frac{1}{4}$

Step 2.2

Subtract $\frac{1}{9}$ from $0$ .

$- \frac{1}{9} + \frac{1}{4}$

Step 3

To write $- \frac{1}{9}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- \frac{1}{9} \cdot \frac{4}{4} + \frac{1}{4}$

Step 4

To write $\frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$- \frac{1}{9} \cdot \frac{4}{4} + \frac{1}{4} \cdot \frac{9}{9}$

Step 5

Write each expression with a common denominator of $36$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.1

Multiply $\frac{1}{9}$ by $\frac{4}{4}$ .

$- \frac{4}{9 \cdot 4} + \frac{1}{4} \cdot \frac{9}{9}$

Step 5.2

Multiply $9$ by $4$ .

$- \frac{4}{36} + \frac{1}{4} \cdot \frac{9}{9}$

Step 5.3

Multiply $\frac{1}{4}$ by $\frac{9}{9}$ .

$- \frac{4}{36} + \frac{9}{4 \cdot 9}$

Step 5.4

Multiply $4$ by $9$ .

$- \frac{4}{36} + \frac{9}{36}$

Step 6

Combine the numerators over the common denominator.

$\frac{- 4 + 9}{36}$

Step 7

Add $- 4$ and $9$ .

$\frac{5}{36}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{36}$

Decimal Form:

$0.13\overline{8}$