Basic Math Examples

${(- \frac{1}{2})}^{2} + \frac{1}{9}$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

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

Tap for more steps...

Step 1.1.1

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

${(- 1)}^{2} {(\frac{1}{2})}^{2} + \frac{1}{9}$

Step 1.1.2

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

${(- 1)}^{2} \frac{1^{2}}{2^{2}} + \frac{1}{9}$

Step 1.2

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

$1 \frac{1^{2}}{2^{2}} + \frac{1}{9}$

Step 1.3

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

$\frac{1^{2}}{2^{2}} + \frac{1}{9}$

Step 1.4

One to any power is one.

$\frac{1}{2^{2}} + \frac{1}{9}$

Step 1.5

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

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

Step 2

To write $\frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

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

Step 3

To write $\frac{1}{9}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

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

Step 4

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

Tap for more steps...

Step 4.1

Multiply $\frac{1}{4}$ by $\frac{9}{9}$ .

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

Step 4.2

Multiply $4$ by $9$ .

$\frac{9}{36} + \frac{1}{9} \cdot \frac{4}{4}$

Step 4.3

Multiply $\frac{1}{9}$ by $\frac{4}{4}$ .

$\frac{9}{36} + \frac{4}{9 \cdot 4}$

Step 4.4

Multiply $9$ by $4$ .

$\frac{9}{36} + \frac{4}{36}$

Step 5

Combine the numerators over the common denominator.

$\frac{9 + 4}{36}$

Step 6

Add $9$ and $4$ .

$\frac{13}{36}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{13}{36}$

Decimal Form:

$0.36\overline{1}$