Algebra Examples

$\frac{1}{4} (x - \frac{2}{5}) - \frac{1}{3} (\frac{3}{4} x - \frac{1}{2})$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$\frac{1}{4} x + \frac{1}{4} (- \frac{2}{5}) - \frac{1}{3} \cdot (\frac{3}{4} x - \frac{1}{2})$

Step 1.2

Combine $\frac{1}{4}$ and $x$ .

$\frac{x}{4} + \frac{1}{4} (- \frac{2}{5}) - \frac{1}{3} \cdot (\frac{3}{4} x - \frac{1}{2})$

Step 1.3

Cancel the common factor of $2$ .

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Step 1.3.1

Move the leading negative in $- \frac{2}{5}$ into the numerator.

$\frac{x}{4} + \frac{1}{4} \cdot \frac{- 2}{5} - \frac{1}{3} \cdot (\frac{3}{4} x - \frac{1}{2})$

Step 1.3.2

Factor $2$ out of $4$ .

$\frac{x}{4} + \frac{1}{2 (2)} \cdot \frac{- 2}{5} - \frac{1}{3} \cdot (\frac{3}{4} x - \frac{1}{2})$

Step 1.3.3

Factor $2$ out of $- 2$ .

$\frac{x}{4} + \frac{1}{2 \cdot 2} \cdot \frac{2 \cdot - 1}{5} - \frac{1}{3} \cdot (\frac{3}{4} x - \frac{1}{2})$

Step 1.3.4

Cancel the common factor.

$\frac{x}{4} + \frac{1}{2 \cdot 2} \cdot \frac{2 \cdot - 1}{5} - \frac{1}{3} \cdot (\frac{3}{4} x - \frac{1}{2})$

Step 1.3.5

Rewrite the expression.

$\frac{x}{4} + \frac{1}{2} \cdot \frac{- 1}{5} - \frac{1}{3} \cdot (\frac{3}{4} x - \frac{1}{2})$

Step 1.4

Multiply $\frac{1}{2}$ by $\frac{- 1}{5}$ .

$\frac{x}{4} + \frac{- 1}{2 \cdot 5} - \frac{1}{3} \cdot (\frac{3}{4} x - \frac{1}{2})$

Step 1.5

Multiply $2$ by $5$ .

$\frac{x}{4} + \frac{- 1}{10} - \frac{1}{3} \cdot (\frac{3}{4} x - \frac{1}{2})$

Step 1.6

Move the negative in front of the fraction.

$\frac{x}{4} - \frac{1}{10} - \frac{1}{3} \cdot (\frac{3}{4} x - \frac{1}{2})$

Step 1.7

Combine $\frac{3}{4}$ and $x$ .

$\frac{x}{4} - \frac{1}{10} - \frac{1}{3} \cdot (\frac{3 x}{4} - \frac{1}{2})$

Step 1.8

Apply the distributive property.

$\frac{x}{4} - \frac{1}{10} - \frac{1}{3} \cdot \frac{3 x}{4} - \frac{1}{3} (- \frac{1}{2})$

Step 1.9

Cancel the common factor of $3$ .

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Step 1.9.1

Move the leading negative in $- \frac{1}{3}$ into the numerator.

$\frac{x}{4} - \frac{1}{10} + \frac{- 1}{3} \cdot \frac{3 x}{4} - \frac{1}{3} (- \frac{1}{2})$

Step 1.9.2

Factor $3$ out of $3 x$ .

$\frac{x}{4} - \frac{1}{10} + \frac{- 1}{3} \cdot \frac{3 (x)}{4} - \frac{1}{3} (- \frac{1}{2})$

Step 1.9.3

Cancel the common factor.

$\frac{x}{4} - \frac{1}{10} + \frac{- 1}{3} \cdot \frac{3 x}{4} - \frac{1}{3} (- \frac{1}{2})$

Step 1.9.4

Rewrite the expression.

$\frac{x}{4} - \frac{1}{10} - 1 \frac{x}{4} - \frac{1}{3} (- \frac{1}{2})$

Step 1.10

Multiply $- \frac{1}{3} (- \frac{1}{2})$ .

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Step 1.10.1

Multiply $- 1$ by $- 1$ .

$\frac{x}{4} - \frac{1}{10} - 1 \frac{x}{4} + 1 (\frac{1}{3}) \frac{1}{2}$

Step 1.10.2

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

$\frac{x}{4} - \frac{1}{10} - 1 \frac{x}{4} + \frac{1}{3} \cdot \frac{1}{2}$

Step 1.10.3

Multiply $\frac{1}{3}$ by $\frac{1}{2}$ .

$\frac{x}{4} - \frac{1}{10} - 1 \frac{x}{4} + \frac{1}{3 \cdot 2}$

Step 1.10.4

Multiply $3$ by $2$ .

$\frac{x}{4} - \frac{1}{10} - 1 \frac{x}{4} + \frac{1}{6}$

Step 1.11

Rewrite $- 1 \frac{x}{4}$ as $- \frac{x}{4}$ .

$\frac{x}{4} - \frac{1}{10} - \frac{x}{4} + \frac{1}{6}$

Step 2

Combine the opposite terms in $\frac{x}{4} - \frac{1}{10} - \frac{x}{4} + \frac{1}{6}$ .

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Step 2.1

Subtract $\frac{x}{4}$ from $\frac{x}{4}$ .

$0 - \frac{1}{10} + \frac{1}{6}$

Step 2.2

Subtract $\frac{1}{10}$ from $0$ .

$- \frac{1}{10} + \frac{1}{6}$

Step 3

To write $- \frac{1}{10}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{1}{10} \cdot \frac{3}{3} + \frac{1}{6}$

Step 4

To write $\frac{1}{6}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{1}{10} \cdot \frac{3}{3} + \frac{1}{6} \cdot \frac{5}{5}$

Step 5

Write each expression with a common denominator of $30$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.1

Multiply $\frac{1}{10}$ by $\frac{3}{3}$ .

$- \frac{3}{10 \cdot 3} + \frac{1}{6} \cdot \frac{5}{5}$

Step 5.2

Multiply $10$ by $3$ .

$- \frac{3}{30} + \frac{1}{6} \cdot \frac{5}{5}$

Step 5.3

Multiply $\frac{1}{6}$ by $\frac{5}{5}$ .

$- \frac{3}{30} + \frac{5}{6 \cdot 5}$

Step 5.4

Multiply $6$ by $5$ .

$- \frac{3}{30} + \frac{5}{30}$

Step 6

Simplify the expression.

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Step 6.1

Combine the numerators over the common denominator.

$\frac{- 3 + 5}{30}$

Step 6.2

Add $- 3$ and $5$ .

$\frac{2}{30}$

Step 7

Cancel the common factor of $2$ and $30$ .

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Step 7.1

Factor $2$ out of $2$ .

$\frac{2 (1)}{30}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $2$ out of $30$ .

$\frac{2 \cdot 1}{2 \cdot 15}$

Step 7.2.2

Cancel the common factor.

$\frac{2 \cdot 1}{2 \cdot 15}$

Step 7.2.3

Rewrite the expression.

$\frac{1}{15}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{15}$

Decimal Form:

$0.0\overline{6}$