Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

Combine the numerators over the common denominator.

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

Step 1.3

Subtract $2$ from $3$ .

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

Step 1.4

Apply the product rule to $\frac{1}{3}$ .

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

Step 1.5

Combine.

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

Step 1.6

Multiply $1$ by $1^{2}$ by adding the exponents.

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Step 1.6.1

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

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Step 1.6.1.1

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

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

Step 1.6.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 1.6.2

Add $1$ and $2$ .

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

Step 1.7

One to any power is one.

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

Step 1.8

Raise $3$ to the power of $2$ .

$\frac{1}{4 \cdot 9} + \frac{1}{3}$

Step 1.9

Multiply $4$ by $9$ .

$\frac{1}{36} + \frac{1}{3}$

Step 2

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{12}{12}$ .

$\frac{1}{36} + \frac{1}{3} \cdot \frac{12}{12}$

Step 3

Write each expression with a common denominator of $36$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{1}{3}$ by $\frac{12}{12}$ .

$\frac{1}{36} + \frac{12}{3 \cdot 12}$

Step 3.2

Multiply $3$ by $12$ .

$\frac{1}{36} + \frac{12}{36}$

Step 4

Combine the numerators over the common denominator.

$\frac{1 + 12}{36}$

Step 5

Add $1$ and $12$ .

$\frac{13}{36}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{13}{36}$

Decimal Form:

$0.36\overline{1}$