Basic Math Examples

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

Step 1

Simplify the numerator.

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Step 1.1

Apply the product rule to $- \frac{1}{2}$ .

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

Step 1.2

Raise $- 1$ to the power of $2$ .

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

Step 1.3

Apply the product rule to $\frac{1}{2}$ .

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

Step 1.4

One to any power is one.

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

Step 1.5

Raise $2$ to the power of $2$ .

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

Step 1.6

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

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

Step 2

To divide by a fraction, multiply by its reciprocal.

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

Step 3

Combine $\frac{1}{4}$ and $- 3$ .

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

Step 4

Move the negative in front of the fraction.

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

Step 5

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 6

To write $- \frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 7

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

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Step 7.1

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

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

Step 7.2

Multiply $2$ by $3$ .

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

Step 7.3

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

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

Step 7.4

Multiply $3$ by $2$ .

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

Step 8

Simplify the expression.

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Step 8.1

Combine the numerators over the common denominator.

$- \frac{3}{4} \cdot \frac{3 - 2}{6}$

Step 8.2

Subtract $2$ from $3$ .

$- \frac{3}{4} \cdot \frac{1}{6}$

Step 9

Cancel the common factor of $3$ .

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Step 9.1

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$\frac{- 3}{4} \cdot \frac{1}{6}$

Step 9.2

Factor $3$ out of $- 3$ .

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

Step 9.3

Factor $3$ out of $6$ .

$\frac{3 \cdot - 1}{4} \cdot \frac{1}{3 \cdot 2}$

Step 9.4

Cancel the common factor.

$\frac{3 \cdot - 1}{4} \cdot \frac{1}{3 \cdot 2}$

Step 9.5

Rewrite the expression.

$\frac{- 1}{4} \cdot \frac{1}{2}$

Step 10

Multiply $\frac{- 1}{4}$ by $\frac{1}{2}$ .

$\frac{- 1}{4 \cdot 2}$

Step 11

Simplify the expression.

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Step 11.1

Multiply $4$ by $2$ .

$\frac{- 1}{8}$

Step 11.2

Move the negative in front of the fraction.

$- \frac{1}{8}$

Step 12

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{8}$

Decimal Form:

$- 0.125$