Solve 4(-1/2)^3-(-1/2)^2-4(-1/2)+1

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

Evaluate

$$\frac{9}{4}=2.25$$

Solution Steps

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

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

Express 4\left(-\frac{1}{8}\right) as a single fraction.

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

Multiply 4 and -1 to get -4.

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

Reduce the fraction \frac{-4}{8} to lowest terms by extracting and canceling out 4.

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

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

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

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

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

Since -\frac{2}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 1 from -2 to get -3.

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

Express 4\left(-\frac{1}{2}\right) as a single fraction.

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

Multiply 4 and -1 to get -4.

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

Divide -4 by 2 to get -2.

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

The opposite of -2 is 2.

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

Convert 2 to fraction \frac{8}{4}.

$$-\frac{3}{4}+\frac{8}{4}+1$$

Since -\frac{3}{4} and \frac{8}{4} have the same denominator, add them by adding their numerators.

$$\frac{-3+8}{4}+1$$

Add -3 and 8 to get 5.

$$\frac{5}{4}+1$$

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

$$\frac{5}{4}+\frac{4}{4}$$

Since \frac{5}{4} and \frac{4}{4} have the same denominator, add them by adding their numerators.

$$\frac{5+4}{4}$$

Add 5 and 4 to get 9.

$$\frac{9}{4}$$

Factor

$$\frac{3 ^ {2}}{2 ^ {2}} = 2\frac{1}{4} = 2.25$$