Algebra Examples

${(- \frac{1}{2})}^{2} + 3 (- \frac{1}{2}) + 5$

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 $- \frac{1}{2}$ .

${(- 1)}^{2} {(\frac{1}{2})}^{2} + 3 (- \frac{1}{2}) + 5$

Step 1.1.2

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

${(- 1)}^{2} \frac{1^{2}}{2^{2}} + 3 (- \frac{1}{2}) + 5$

Step 1.2

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

$1 \frac{1^{2}}{2^{2}} + 3 (- \frac{1}{2}) + 5$

Step 1.3

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

$\frac{1^{2}}{2^{2}} + 3 (- \frac{1}{2}) + 5$

Step 1.4

One to any power is one.

$\frac{1}{2^{2}} + 3 (- \frac{1}{2}) + 5$

Step 1.5

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

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

Step 1.6

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

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Step 1.6.1

Multiply $- 1$ by $3$ .

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

Step 1.6.2

Combine $- 3$ and $\frac{1}{2}$ .

$\frac{1}{4} + \frac{- 3}{2} + 5$

Step 1.7

Move the negative in front of the fraction.

$\frac{1}{4} - \frac{3}{2} + 5$

Step 2

Find the common denominator.

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

Write $5$ as a fraction with denominator $1$ .

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

Step 2.4

Multiply $\frac{5}{1}$ by $\frac{4}{4}$ .

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

Step 2.5

Multiply $\frac{5}{1}$ by $\frac{4}{4}$ .

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

Step 2.6

Multiply $2$ by $2$ .

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

Step 3

Combine the numerators over the common denominator.

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

Step 4

Simplify each term.

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Step 4.1

Multiply $- 3$ by $2$ .

$\frac{1 - 6 + 5 \cdot 4}{4}$

Step 4.2

Multiply $5$ by $4$ .

$\frac{1 - 6 + 20}{4}$

Step 5

Simplify by adding and subtracting.

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Step 5.1

Subtract $6$ from $1$ .

$\frac{- 5 + 20}{4}$

Step 5.2

Add $- 5$ and $20$ .

$\frac{15}{4}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{15}{4}$

Decimal Form:

$3.75$

Mixed Number Form:

$3 \frac{3}{4}$