Algebra Examples

$\frac{1}{2} {(\frac{5}{6})}^{2} + \frac{2}{9}$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Apply the product rule to $\frac{5}{6}$ .

$\frac{1}{2} \cdot \frac{5^{2}}{6^{2}} + \frac{2}{9}$

Step 1.2

Combine.

$\frac{1 \cdot 5^{2}}{2 \cdot 6^{2}} + \frac{2}{9}$

Step 1.3

Multiply $5^{2}$ by $1$ .

$\frac{5^{2}}{2 \cdot 6^{2}} + \frac{2}{9}$

Step 1.4

Raise $6$ to the power of $2$ .

$\frac{5^{2}}{2 \cdot 36} + \frac{2}{9}$

Step 1.5

Raise $5$ to the power of $2$ .

$\frac{25}{2 \cdot 36} + \frac{2}{9}$

Step 1.6

Multiply $2$ by $36$ .

$\frac{25}{72} + \frac{2}{9}$

Step 2

To write $\frac{2}{9}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{25}{72} + \frac{2}{9} \cdot \frac{8}{8}$

Step 3

Write each expression with a common denominator of $72$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 3.1

Multiply $\frac{2}{9}$ by $\frac{8}{8}$ .

$\frac{25}{72} + \frac{2 \cdot 8}{9 \cdot 8}$

Step 3.2

Multiply $9$ by $8$ .

$\frac{25}{72} + \frac{2 \cdot 8}{72}$

Step 4

Combine the numerators over the common denominator.

$\frac{25 + 2 \cdot 8}{72}$

Step 5

Simplify the numerator.

Tap for more steps...

Step 5.1

Multiply $2$ by $8$ .

$\frac{25 + 16}{72}$

Step 5.2

Add $25$ and $16$ .

$\frac{41}{72}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{41}{72}$

Decimal Form:

$0.569\overline{4}$