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

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

Simplify each term.

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

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

Combine.

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

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

$\frac{5^{2}}{2 \cdot 6^{2}} + \frac{5}{8}$

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

$\frac{5^{2}}{2 \cdot 36} + \frac{5}{8}$

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

$\frac{25}{2 \cdot 36} + \frac{5}{8}$

Multiply $2$ by $36$ .

$\frac{25}{72} + \frac{5}{8}$

To write $\frac{5}{8}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{25}{72} + \frac{5}{8} \cdot \frac{9}{9}$

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

Multiply $\frac{5}{8}$ by $\frac{9}{9}$ .

$\frac{25}{72} + \frac{5 \cdot 9}{8 \cdot 9}$

Multiply $8$ by $9$ .

$\frac{25}{72} + \frac{5 \cdot 9}{72}$

Combine the numerators over the common denominator.

$\frac{25 + 5 \cdot 9}{72}$

Simplify the numerator.

Multiply $5$ by $9$ .

$\frac{25 + 45}{72}$

Add $25$ and $45$ .

$\frac{70}{72}$

Cancel the common factor of $70$ and $72$ .

Factor $2$ out of $70$ .

$\frac{2 (35)}{72}$

Cancel the common factors.

Factor $2$ out of $72$ .

$\frac{2 \cdot 35}{2 \cdot 36}$

Cancel the common factor.

$\frac{2 \cdot 35}{2 \cdot 36}$

Rewrite the expression.

$\frac{35}{36}$

The result can be shown in multiple forms.

Exact Form:

$\frac{35}{36}$

Decimal Form:

$0.97\overline{2}$