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

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

Evaluate

$$-\frac{11}{8}=-1.375$$

Solution Steps

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

$$3\times \frac{1}{8}-\left(\frac{1}{2}\right)^{2}+\frac{1}{2}-2$$

Multiply 3 and \frac{1}{8} to get \frac{3}{8}.

$$\frac{3}{8}-\left(\frac{1}{2}\right)^{2}+\frac{1}{2}-2$$

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

$$\frac{3}{8}-\frac{1}{4}+\frac{1}{2}-2$$

Least common multiple of 8 and 4 is 8. Convert \frac{3}{8} and \frac{1}{4} to fractions with denominator 8.

$$\frac{3}{8}-\frac{2}{8}+\frac{1}{2}-2$$

Since \frac{3}{8} and \frac{2}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-2}{8}+\frac{1}{2}-2$$

Subtract 2 from 3 to get 1.

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

Least common multiple of 8 and 2 is 8. Convert \frac{1}{8} and \frac{1}{2} to fractions with denominator 8.

$$\frac{1}{8}+\frac{4}{8}-2$$

Since \frac{1}{8} and \frac{4}{8} have the same denominator, add them by adding their numerators.

$$\frac{1+4}{8}-2$$

Add 1 and 4 to get 5.

$$\frac{5}{8}-2$$

Convert 2 to fraction \frac{16}{8}.

$$\frac{5}{8}-\frac{16}{8}$$

Since \frac{5}{8} and \frac{16}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5-16}{8}$$

Subtract 16 from 5 to get -11.

$$-\frac{11}{8}$$

Factor

$$-\frac{11}{8} = -1\frac{3}{8} = -1.375$$