Evaluate 1/2(5/6)^2-1/8

$\frac{1}{2} {(\frac{5}{6})}^{2} - \frac{1}{8}$

Simplify each term.

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

$\frac{1}{2} \cdot \frac{5^{2}}{6^{2}} - \frac{1}{8}$

Combine.

$\frac{1 \cdot 5^{2}}{2 \cdot 6^{2}} - \frac{1}{8}$

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

$\frac{5^{2}}{2 \cdot 6^{2}} - \frac{1}{8}$

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

$\frac{5^{2}}{2 \cdot 36} - \frac{1}{8}$

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

$\frac{25}{2 \cdot 36} - \frac{1}{8}$

Multiply $2$ by $36$ .

$\frac{25}{72} - \frac{1}{8}$

To write $- \frac{1}{8}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{25}{72} - \frac{1}{8} \cdot \frac{9}{9}$

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

Multiply $\frac{1}{8}$ by $\frac{9}{9}$ .

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

Multiply $8$ by $9$ .

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

Simplify the expression.

Combine the numerators over the common denominator.

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

Subtract $9$ from $25$ .

$\frac{16}{72}$

Cancel the common factor of $16$ and $72$ .

Factor $8$ out of $16$ .

$\frac{8 (2)}{72}$

Cancel the common factors.

Factor $8$ out of $72$ .

$\frac{8 \cdot 2}{8 \cdot 9}$

Cancel the common factor.

$\frac{8 \cdot 2}{8 \cdot 9}$

Rewrite the expression.

$\frac{2}{9}$

The result can be shown in multiple forms.

Exact Form:

$\frac{2}{9}$

Decimal Form:

$0.\overline{2}$