Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.2.1

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

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

Step 1.2.2

Multiply $2$ by $2$ .

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

Step 1.3

Combine the numerators over the common denominator.

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

Step 1.4

Subtract $3$ from $2$ .

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

Step 1.5

Move the negative in front of the fraction.

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

Step 1.6

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

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Step 1.6.1

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

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

Step 1.6.2

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

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

Step 1.7

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

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

Step 1.8

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

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

Step 1.9

One to any power is one.

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

Step 1.10

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

$\frac{1}{4} + 4 (\frac{1}{16})$

Step 1.11

Cancel the common factor of $4$ .

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Step 1.11.1

Factor $4$ out of $16$ .

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

Step 1.11.2

Cancel the common factor.

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

Step 1.11.3

Rewrite the expression.

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

Step 2

Simplify terms.

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Step 2.1

Combine the numerators over the common denominator.

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

Step 2.2

Add $1$ and $1$ .

$\frac{2}{4}$

Step 2.3

Cancel the common factor of $2$ and $4$ .

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Step 2.3.1

Factor $2$ out of $2$ .

$\frac{2 (1)}{4}$

Step 2.3.2

Cancel the common factors.

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Step 2.3.2.1

Factor $2$ out of $4$ .

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

Step 2.3.2.2

Cancel the common factor.

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

Step 2.3.2.3

Rewrite the expression.

$\frac{1}{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2}$

Decimal Form:

$0.5$