Basic Math Examples

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

Step 1

Simplify each term.

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Step 1.1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 1.1.1

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

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

Step 1.1.2

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

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

Step 1.2

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

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

Step 1.3

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

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

Step 1.4

One to any power is one.

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

Step 1.5

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

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

Step 1.6

Cancel the common factor of $4$ .

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Step 1.6.1

Factor $4$ out of $- 4$ .

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

Step 1.6.2

Cancel the common factor.

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

Step 1.6.3

Rewrite the expression.

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

Step 1.7

Multiply $- 1$ by $3$ .

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

Step 1.8

Cancel the common factor of $3$ .

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Step 1.8.1

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

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

Step 1.8.2

Factor $3$ out of $- 3$ .

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

Step 1.8.3

Cancel the common factor.

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

Step 1.8.4

Rewrite the expression.

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

Step 1.9

Multiply $- 1$ by $- 1$ .

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

Step 2

Simplify the expression.

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Step 2.1

Write $1$ as a fraction with a common denominator.

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

Step 2.2

Combine the numerators over the common denominator.

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

Step 2.3

Add $1$ and $4$ .

$\frac{5}{4}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{4}$

Decimal Form:

$1.25$

Mixed Number Form:

$1 \frac{1}{4}$