Evaluate 7/9+1/2(5/6)^2

$\frac{7}{9} + \frac{1}{2} {(\frac{5}{6})}^{2}$

Step 1

Simplify each term.

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

$\frac{7}{9} + \frac{1}{2} \cdot \frac{5^{2}}{6^{2}}$

Combine.

$\frac{7}{9} + \frac{1 \cdot 5^{2}}{2 \cdot 6^{2}}$

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

$\frac{7}{9} + \frac{5^{2}}{2 \cdot 6^{2}}$

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

$\frac{7}{9} + \frac{5^{2}}{2 \cdot 36}$

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

$\frac{7}{9} + \frac{25}{2 \cdot 36}$

Multiply $2$ by $36$ .

$\frac{7}{9} + \frac{25}{72}$

Step 2

To write $\frac{7}{9}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{7}{9} \cdot \frac{8}{8} + \frac{25}{72}$

Step 3

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

Multiply $\frac{7}{9}$ by $\frac{8}{8}$ .

$\frac{7 \cdot 8}{9 \cdot 8} + \frac{25}{72}$

Multiply $9$ by $8$ .

$\frac{7 \cdot 8}{72} + \frac{25}{72}$

Step 4

Combine the numerators over the common denominator.

$\frac{7 \cdot 8 + 25}{72}$

Step 5

Simplify the numerator.

Multiply $7$ by $8$ .

$\frac{56 + 25}{72}$

Add $56$ and $25$ .

$\frac{81}{72}$

Step 6

Cancel the common factor of $81$ and $72$ .

Factor $9$ out of $81$ .

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

Cancel the common factors.

Factor $9$ out of $72$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{9}{8}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{9}{8}$

Decimal Form:

$1.125$

Mixed Number Form:

$1 \frac{1}{8}$

Evaluate 7/9+1/2(5/6)^2

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