Evaluate (1/5)^2+11/20-1/4

${(\frac{1}{5})}^{2} + \frac{11}{20} - \frac{1}{4}$

Step 1

Find the common denominator.

Write ${(\frac{1}{5})}^{2}$ as a fraction with denominator $1$ .

$\frac{{(\frac{1}{5})}^{2}}{1} + \frac{11}{20} - \frac{1}{4}$

Multiply $\frac{{(\frac{1}{5})}^{2}}{1}$ by $\frac{20}{20}$ .

$\frac{{(\frac{1}{5})}^{2}}{1} \cdot \frac{20}{20} + \frac{11}{20} - \frac{1}{4}$

Multiply $\frac{{(\frac{1}{5})}^{2}}{1}$ by $\frac{20}{20}$ .

$\frac{{(\frac{1}{5})}^{2} \cdot 20}{20} + \frac{11}{20} - \frac{1}{4}$

Multiply $\frac{1}{4}$ by $\frac{5}{5}$ .

$\frac{{(\frac{1}{5})}^{2} \cdot 20}{20} + \frac{11}{20} - (\frac{1}{4} \cdot \frac{5}{5})$

Multiply $\frac{1}{4}$ by $\frac{5}{5}$ .

$\frac{{(\frac{1}{5})}^{2} \cdot 20}{20} + \frac{11}{20} - \frac{5}{4 \cdot 5}$

Multiply $4$ by $5$ .

$\frac{{(\frac{1}{5})}^{2} \cdot 20}{20} + \frac{11}{20} - \frac{5}{20}$

Step 2

Combine the numerators over the common denominator.

$\frac{{(\frac{1}{5})}^{2} \cdot 20 + 11 - 5}{20}$

Step 3

Simplify each term.

Apply the product rule to $\frac{1}{5}$ .

$\frac{\frac{1^{2}}{5^{2}} \cdot 20 + 11 - 5}{20}$

One to any power is one.

$\frac{\frac{1}{5^{2}} \cdot 20 + 11 - 5}{20}$

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

$\frac{\frac{1}{25} \cdot 20 + 11 - 5}{20}$

Cancel the common factor of $5$ .

Factor $5$ out of $25$ .

$\frac{\frac{1}{5 (5)} \cdot 20 + 11 - 5}{20}$

Factor $5$ out of $20$ .

$\frac{\frac{1}{5 \cdot 5} \cdot (5 \cdot 4) + 11 - 5}{20}$

Cancel the common factor.

$\frac{\frac{1}{5 \cdot 5} \cdot (5 \cdot 4) + 11 - 5}{20}$

Rewrite the expression.

$\frac{\frac{1}{5} \cdot 4 + 11 - 5}{20}$

Combine $\frac{1}{5}$ and $4$ .

$\frac{\frac{4}{5} + 11 - 5}{20}$

Step 4

Find the common denominator.

Write $11$ as a fraction with denominator $1$ .

$\frac{\frac{4}{5} + \frac{11}{1} - 5}{20}$

Multiply $\frac{11}{1}$ by $\frac{5}{5}$ .

$\frac{\frac{4}{5} + \frac{11}{1} \cdot \frac{5}{5} - 5}{20}$

Multiply $\frac{11}{1}$ by $\frac{5}{5}$ .

$\frac{\frac{4}{5} + \frac{11 \cdot 5}{5} - 5}{20}$

Write $- 5$ as a fraction with denominator $1$ .

$\frac{\frac{4}{5} + \frac{11 \cdot 5}{5} + \frac{- 5}{1}}{20}$

Multiply $\frac{- 5}{1}$ by $\frac{5}{5}$ .

$\frac{\frac{4}{5} + \frac{11 \cdot 5}{5} + \frac{- 5}{1} \cdot \frac{5}{5}}{20}$

Multiply $\frac{- 5}{1}$ by $\frac{5}{5}$ .

$\frac{\frac{4}{5} + \frac{11 \cdot 5}{5} + \frac{- 5 \cdot 5}{5}}{20}$

Step 5

Combine the numerators over the common denominator.

$\frac{\frac{4 + 11 \cdot 5 - 5 \cdot 5}{5}}{20}$

Step 6

Simplify each term.

Multiply $11$ by $5$ .

$\frac{\frac{4 + 55 - 5 \cdot 5}{5}}{20}$

Multiply $- 5$ by $5$ .

$\frac{\frac{4 + 55 - 25}{5}}{20}$

Step 7

Simplify by adding and subtracting.

Add $4$ and $55$ .

$\frac{\frac{59 - 25}{5}}{20}$

Subtract $25$ from $59$ .

$\frac{\frac{34}{5}}{20}$

Step 8

Multiply the numerator by the reciprocal of the denominator.

$\frac{34}{5} \cdot \frac{1}{20}$

Step 9

Cancel the common factor of $2$ .

Factor $2$ out of $34$ .

$\frac{2 (17)}{5} \cdot \frac{1}{20}$

Factor $2$ out of $20$ .

$\frac{2 \cdot 17}{5} \cdot \frac{1}{2 \cdot 10}$

Cancel the common factor.

$\frac{2 \cdot 17}{5} \cdot \frac{1}{2 \cdot 10}$

Rewrite the expression.

$\frac{17}{5} \cdot \frac{1}{10}$

Step 10

Multiply $\frac{17}{5}$ by $\frac{1}{10}$ .

$\frac{17}{5 \cdot 10}$

Step 11

Multiply $5$ by $10$ .

$\frac{17}{50}$

Step 12

The result can be shown in multiple forms.

Exact Form:

$\frac{17}{50}$

Decimal Form:

$0.34$

Evaluate (1/5)^2+11/20-1/4

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