Basic Math Examples

$\frac{1}{2} - \frac{\frac{1}{4} + \frac{2}{3}}{1 - (\frac{1}{6})}$

Step 1

Simplify each term.

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Step 1.1

Multiply the numerator and denominator of the fraction by $12$ .

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Step 1.1.1

Multiply $\frac{\frac{1}{4} + \frac{2}{3}}{1 - \frac{1}{6}}$ by $\frac{12}{12}$ .

$\frac{1}{2} - (\frac{12}{12} \cdot \frac{\frac{1}{4} + \frac{2}{3}}{1 - \frac{1}{6}})$

Step 1.1.2

Combine.

$\frac{1}{2} - \frac{12 (\frac{1}{4} + \frac{2}{3})}{12 (1 - \frac{1}{6})}$

Step 1.2

Apply the distributive property.

$\frac{1}{2} - \frac{12 (\frac{1}{4}) + 12 (\frac{2}{3})}{12 \cdot 1 + 12 (- \frac{1}{6})}$

Step 1.3

Simplify by cancelling.

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Step 1.3.1

Cancel the common factor of $4$ .

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Step 1.3.1.1

Factor $4$ out of $12$ .

$\frac{1}{2} - \frac{4 (3) \frac{1}{4} + 12 (\frac{2}{3})}{12 \cdot 1 + 12 (- \frac{1}{6})}$

Step 1.3.1.2

Cancel the common factor.

$\frac{1}{2} - \frac{4 \cdot 3 \frac{1}{4} + 12 (\frac{2}{3})}{12 \cdot 1 + 12 (- \frac{1}{6})}$

Step 1.3.1.3

Rewrite the expression.

$\frac{1}{2} - \frac{3 + 12 (\frac{2}{3})}{12 \cdot 1 + 12 (- \frac{1}{6})}$

Step 1.3.2

Cancel the common factor of $3$ .

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Step 1.3.2.1

Factor $3$ out of $12$ .

$\frac{1}{2} - \frac{3 + 3 (4) \frac{2}{3}}{12 \cdot 1 + 12 (- \frac{1}{6})}$

Step 1.3.2.2

Cancel the common factor.

$\frac{1}{2} - \frac{3 + 3 \cdot 4 \frac{2}{3}}{12 \cdot 1 + 12 (- \frac{1}{6})}$

Step 1.3.2.3

Rewrite the expression.

$\frac{1}{2} - \frac{3 + 4 \cdot 2}{12 \cdot 1 + 12 (- \frac{1}{6})}$

Step 1.3.3

Multiply $4$ by $2$ .

$\frac{1}{2} - \frac{3 + 8}{12 \cdot 1 + 12 (- \frac{1}{6})}$

Step 1.3.4

Cancel the common factor of $6$ .

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Step 1.3.4.1

Move the leading negative in $- \frac{1}{6}$ into the numerator.

$\frac{1}{2} - \frac{3 + 8}{12 \cdot 1 + 12 (\frac{- 1}{6})}$

Step 1.3.4.2

Factor $6$ out of $12$ .

$\frac{1}{2} - \frac{3 + 8}{12 \cdot 1 + 6 (2) \frac{- 1}{6}}$

Step 1.3.4.3

Cancel the common factor.

$\frac{1}{2} - \frac{3 + 8}{12 \cdot 1 + 6 \cdot 2 \frac{- 1}{6}}$

Step 1.3.4.4

Rewrite the expression.

$\frac{1}{2} - \frac{3 + 8}{12 \cdot 1 + 2 \cdot - 1}$

Step 1.3.5

Multiply $2$ by $- 1$ .

$\frac{1}{2} - \frac{3 + 8}{12 \cdot 1 - 2}$

Step 1.4

Add $3$ and $8$ .

$\frac{1}{2} - \frac{11}{12 \cdot 1 - 2}$

Step 1.5

Simplify the denominator.

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Step 1.5.1

Multiply $12$ by $1$ .

$\frac{1}{2} - \frac{11}{12 - 2}$

Step 1.5.2

Subtract $2$ from $12$ .

$\frac{1}{2} - \frac{11}{10}$

Step 2

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{1}{2} \cdot \frac{5}{5} - \frac{11}{10}$

Step 3

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

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

$\frac{5}{2 \cdot 5} - \frac{11}{10}$

Step 3.2

Multiply $2$ by $5$ .

$\frac{5}{10} - \frac{11}{10}$

Step 4

Simplify the expression.

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Step 4.1

Combine the numerators over the common denominator.

$\frac{5 - 11}{10}$

Step 4.2

Subtract $11$ from $5$ .

$\frac{- 6}{10}$

Step 5

Cancel the common factor of $- 6$ and $10$ .

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Step 5.1

Factor $2$ out of $- 6$ .

$\frac{2 (- 3)}{10}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $2$ out of $10$ .

$\frac{2 \cdot - 3}{2 \cdot 5}$

Step 5.2.2

Cancel the common factor.

$\frac{2 \cdot - 3}{2 \cdot 5}$

Step 5.2.3

Rewrite the expression.

$\frac{- 3}{5}$

Step 6

Move the negative in front of the fraction.

$- \frac{3}{5}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{3}{5}$

Decimal Form:

$- 0.6$