Solve 2(1/2)^3+4(-1/2)^2-3(-1/2)+6

$$2 ( \frac { 1 } { 2 } ) ^ { 3 } + 4 ( - \frac { 1 } { 2 } ) ^ { 2 } - 3 ( - \frac { 1 } { 2 } ) + 6$$

Evaluate

$$\frac{35}{4}=8.75$$

Solution Steps

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

$$2\times \frac{1}{8}+4\left(-\frac{1}{2}\right)^{2}-3\left(-\frac{1}{2}\right)+6$$

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

$$\frac{2}{8}+4\left(-\frac{1}{2}\right)^{2}-3\left(-\frac{1}{2}\right)+6$$

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

$$\frac{1}{4}+4\left(-\frac{1}{2}\right)^{2}-3\left(-\frac{1}{2}\right)+6$$

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

$$\frac{1}{4}+4\times \frac{1}{4}-3\left(-\frac{1}{2}\right)+6$$

Cancel out 4 and 4.

$$\frac{1}{4}+1-3\left(-\frac{1}{2}\right)+6$$

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

$$\frac{1}{4}+\frac{4}{4}-3\left(-\frac{1}{2}\right)+6$$

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

$$\frac{1+4}{4}-3\left(-\frac{1}{2}\right)+6$$

Add 1 and 4 to get 5.

$$\frac{5}{4}-3\left(-\frac{1}{2}\right)+6$$

Express 3\left(-\frac{1}{2}\right) as a single fraction.

$$\frac{5}{4}-\frac{3\left(-1\right)}{2}+6$$

Multiply 3 and -1 to get -3.

$$\frac{5}{4}-\frac{-3}{2}+6$$

Fraction \frac{-3}{2} can be rewritten as -\frac{3}{2} by extracting the negative sign.

$$\frac{5}{4}-\left(-\frac{3}{2}\right)+6$$

The opposite of -\frac{3}{2} is \frac{3}{2}.

$$\frac{5}{4}+\frac{3}{2}+6$$

Least common multiple of 4 and 2 is 4. Convert \frac{5}{4} and \frac{3}{2} to fractions with denominator 4.

$$\frac{5}{4}+\frac{6}{4}+6$$

Since \frac{5}{4} and \frac{6}{4} have the same denominator, add them by adding their numerators.

$$\frac{5+6}{4}+6$$

Add 5 and 6 to get 11.

$$\frac{11}{4}+6$$

Convert 6 to fraction \frac{24}{4}.

$$\frac{11}{4}+\frac{24}{4}$$

Since \frac{11}{4} and \frac{24}{4} have the same denominator, add them by adding their numerators.

$$\frac{11+24}{4}$$

Add 11 and 24 to get 35.

$$\frac{35}{4}$$

Factor

$$\frac{5 \cdot 7}{2 ^ {2}} = 8\frac{3}{4} = 8.75$$