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

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

Evaluate

$$\frac{3}{8}=0.375$$

Solution Steps

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

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

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

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

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

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

Multiply 2 and \frac{1}{4} to get \frac{2}{4}.

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

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

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

Least common multiple of 8 and 2 is 8. Convert \frac{3}{8} and \frac{1}{2} to fractions with denominator 8.

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

Since \frac{3}{8} and \frac{4}{8} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 4 from 3 to get -1.

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

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

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

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

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

Add -1 and 4 to get 3.

$$\frac{3}{8}$$

Factor

$$\frac{3}{2 ^ {3}} = 0.375$$