Solve 2{left(1/2right)}^3-4{left(1/2right)}^2+1/2-1

$$2 { \left( \frac{ 1 }{ 2 } \right) }^{ 3 } -4 { \left( \frac{ 1 }{ 2 } \right) }^{ 2 } + \frac{ 1 }{ 2 } -1$$

Evaluate

$$-\frac{5}{4}=-1.25$$

Solution Steps

Calculate \frac{1}{2} to the power of 3 and get \frac{1}{8}.

$$2\times \frac{1}{8}-4\times \left(\frac{1}{2}\right)^{2}+\frac{1}{2}-1$$

Multiply 2 and \frac{1}{8} to get \frac{2}{8}.

$$\frac{2}{8}-4\times \left(\frac{1}{2}\right)^{2}+\frac{1}{2}-1$$

Reduce the fraction \frac{2}{8} to lowest terms by extracting and canceling out 2.

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

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

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

Cancel out 4 and 4.

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

Convert 1 to fraction \frac{4}{4}.

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

Since \frac{1}{4} and \frac{4}{4} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 4 from 1 to get -3.

$$-\frac{3}{4}+\frac{1}{2}-1$$

Least common multiple of 4 and 2 is 4. Convert -\frac{3}{4} and \frac{1}{2} to fractions with denominator 4.

$$-\frac{3}{4}+\frac{2}{4}-1$$

Since -\frac{3}{4} and \frac{2}{4} have the same denominator, add them by adding their numerators.

$$\frac{-3+2}{4}-1$$

Add -3 and 2 to get -1.

$$-\frac{1}{4}-1$$

Convert 1 to fraction \frac{4}{4}.

$$-\frac{1}{4}-\frac{4}{4}$$

Since -\frac{1}{4} and \frac{4}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-1-4}{4}$$

Subtract 4 from -1 to get -5.

$$-\frac{5}{4}$$

Factor

$$-\frac{5}{4} = -1\frac{1}{4} = -1.25$$