Precalculus Examples

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

Step 1

Find the common denominator.

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Step 1.1

Write $2 {(- \frac{1}{4})}^{2}$ as a fraction with denominator $1$ .

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

Step 1.2

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

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

Step 1.3

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

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

Step 1.4

Write $2$ as a fraction with denominator $1$ .

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

Step 1.5

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

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

Step 1.6

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

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

Step 2

Combine the numerators over the common denominator.

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

Step 3

Simplify each term.

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Step 3.1

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

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Step 3.1.1

Apply the product rule to $- \frac{1}{4}$ .

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

Step 3.1.2

Apply the product rule to $\frac{1}{4}$ .

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

Step 3.2

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

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

Step 3.3

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

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

Step 3.4

One to any power is one.

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

Step 3.5

Raise $4$ to the power of $2$ .

$\frac{2 (\frac{1}{16}) \cdot 4 - 1 + 2 \cdot 4}{4}$

Step 3.6

Cancel the common factor of $2$ .

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Step 3.6.1

Factor $2$ out of $16$ .

$\frac{2 \frac{1}{2 (8)} \cdot 4 - 1 + 2 \cdot 4}{4}$

Step 3.6.2

Cancel the common factor.

$\frac{2 \frac{1}{2 \cdot 8} \cdot 4 - 1 + 2 \cdot 4}{4}$

Step 3.6.3

Rewrite the expression.

$\frac{\frac{1}{8} \cdot 4 - 1 + 2 \cdot 4}{4}$

Step 3.7

Cancel the common factor of $4$ .

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Step 3.7.1

Factor $4$ out of $8$ .

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

Step 3.7.2

Cancel the common factor.

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

Step 3.7.3

Rewrite the expression.

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

Step 3.8

Multiply $2$ by $4$ .

$\frac{\frac{1}{2} - 1 + 8}{4}$

Step 4

Find the common denominator.

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Step 4.1

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

$\frac{\frac{1}{2} + \frac{- 1}{1} + 8}{4}$

Step 4.2

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

$\frac{\frac{1}{2} + \frac{- 1}{1} \cdot \frac{2}{2} + 8}{4}$

Step 4.3

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

$\frac{\frac{1}{2} + \frac{- 1 \cdot 2}{2} + 8}{4}$

Step 4.4

Write $8$ as a fraction with denominator $1$ .

$\frac{\frac{1}{2} + \frac{- 1 \cdot 2}{2} + \frac{8}{1}}{4}$

Step 4.5

Multiply $\frac{8}{1}$ by $\frac{2}{2}$ .

$\frac{\frac{1}{2} + \frac{- 1 \cdot 2}{2} + \frac{8}{1} \cdot \frac{2}{2}}{4}$

Step 4.6

Multiply $\frac{8}{1}$ by $\frac{2}{2}$ .

$\frac{\frac{1}{2} + \frac{- 1 \cdot 2}{2} + \frac{8 \cdot 2}{2}}{4}$

Step 5

Combine the numerators over the common denominator.

$\frac{\frac{1 - 1 \cdot 2 + 8 \cdot 2}{2}}{4}$

Step 6

Simplify each term.

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Step 6.1

Multiply $- 1$ by $2$ .

$\frac{\frac{1 - 2 + 8 \cdot 2}{2}}{4}$

Step 6.2

Multiply $8$ by $2$ .

$\frac{\frac{1 - 2 + 16}{2}}{4}$

Step 7

Simplify by adding and subtracting.

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Step 7.1

Subtract $2$ from $1$ .

$\frac{\frac{- 1 + 16}{2}}{4}$

Step 7.2

Add $- 1$ and $16$ .

$\frac{\frac{15}{2}}{4}$

Step 8

Multiply the numerator by the reciprocal of the denominator.

$\frac{15}{2} \cdot \frac{1}{4}$

Step 9

Multiply $\frac{15}{2} \cdot \frac{1}{4}$ .

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Step 9.1

Multiply $\frac{15}{2}$ by $\frac{1}{4}$ .

$\frac{15}{2 \cdot 4}$

Step 9.2

Multiply $2$ by $4$ .

$\frac{15}{8}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{15}{8}$

Decimal Form:

$1.875$

Mixed Number Form:

$1 \frac{7}{8}$