Evaluate 1/2(5/6)^2-2/9

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

Simplify each term.

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

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

Combine.

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

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

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

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

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

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

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

Multiply $2$ by $36$ .

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

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

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

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

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

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

Multiply $9$ by $8$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $- 2$ by $8$ .

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

Subtract $16$ from $25$ .

$\frac{9}{72}$

Cancel the common factor of $9$ and $72$ .

Factor $9$ out of $9$ .

$\frac{9 (1)}{72}$

Cancel the common factors.

Factor $9$ out of $72$ .

$\frac{9 \cdot 1}{9 \cdot 8}$

Cancel the common factor.

$\frac{9 \cdot 1}{9 \cdot 8}$

Rewrite the expression.

$\frac{1}{8}$

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{8}$

Decimal Form:

$0.125$