Solve 1/4{left(frac{1{2}right)}^2-41/2+1}

$$\frac{ 1 }{ 4 { \left( \frac{ 1 }{ 2 } \right) }^{ 2 } -4 \frac{ 1 }{ 2 } +1 }$$

Evaluate

$$-\frac{2}{5}=-0.4$$

Solution Steps

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$\frac{1}{4\times \frac{1}{4}-\frac{4\times 2+1}{2}+1}$$

Cancel out 4 and 4.

$$\frac{1}{1-\frac{4\times 2+1}{2}+1}$$

Multiply 4 and 2 to get 8.

$$\frac{1}{1-\frac{8+1}{2}+1}$$

Add 8 and 1 to get 9.

$$\frac{1}{1-\frac{9}{2}+1}$$

Convert 1 to fraction \frac{2}{2}.

$$\frac{1}{\frac{2}{2}-\frac{9}{2}+1}$$

Since \frac{2}{2} and \frac{9}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{\frac{2-9}{2}+1}$$

Subtract 9 from 2 to get -7.

$$\frac{1}{-\frac{7}{2}+1}$$

Convert 1 to fraction \frac{2}{2}.

$$\frac{1}{-\frac{7}{2}+\frac{2}{2}}$$

Since -\frac{7}{2} and \frac{2}{2} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{-7+2}{2}}$$

Add -7 and 2 to get -5.

$$\frac{1}{-\frac{5}{2}}$$

Divide 1 by -\frac{5}{2} by multiplying 1 by the reciprocal of -\frac{5}{2}.

$$1\left(-\frac{2}{5}\right)$$

Multiply 1 and -\frac{2}{5} to get -\frac{2}{5}.

$$-\frac{2}{5}$$

Factor

$$-\frac{2}{5} = -0.4$$