Evaluate (10/11)^2-1/11

${(\frac{10}{11})}^{2} - \frac{1}{11}$

Step 1

Simplify each term.

Apply the product rule to $\frac{10}{11}$ .

$\frac{10^{2}}{11^{2}} - \frac{1}{11}$

Raise $10$ to the power of $2$ .

$\frac{100}{11^{2}} - \frac{1}{11}$

Raise $11$ to the power of $2$ .

$\frac{100}{121} - \frac{1}{11}$

Step 2

To write $- \frac{1}{11}$ as a fraction with a common denominator, multiply by $\frac{11}{11}$ .

$\frac{100}{121} - \frac{1}{11} \cdot \frac{11}{11}$

Step 3

Write each expression with a common denominator of $121$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{11}$ by $\frac{11}{11}$ .

$\frac{100}{121} - \frac{11}{11 \cdot 11}$

Multiply $11$ by $11$ .

$\frac{100}{121} - \frac{11}{121}$

Step 4

Combine the numerators over the common denominator.

$\frac{100 - 11}{121}$

Step 5

Subtract $11$ from $100$ .

$\frac{89}{121}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{89}{121}$

Decimal Form:

$0.73553719 \dots$