Solve -1^2014-left(1+0.5right)1/3+left|-6right|div2

$${ -1 }^{ 2014 } - \left( 1+0.5 \right) \frac{ 1 }{ 3 } + \left| -6 \right| \div 2$$

Evaluate

$$3.5$$

Solution Steps

Calculate -1 to the power of 2014 and get 1.

$$1-\left(1+0.5\right)\times \frac{1}{3}+\frac{|-6|}{2}$$

Add 1 and 0.5 to get 1.5.

$$1-1.5\times \frac{1}{3}+\frac{|-6|}{2}$$

Convert decimal number 1.5 to fraction \frac{15}{10}. Reduce the fraction \frac{15}{10} to lowest terms by extracting and canceling out 5.

$$1-\frac{3}{2}\times \frac{1}{3}+\frac{|-6|}{2}$$

Multiply \frac{3}{2} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$1-\frac{3\times 1}{2\times 3}+\frac{|-6|}{2}$$

Cancel out 3 in both numerator and denominator.

$$1-\frac{1}{2}+\frac{|-6|}{2}$$

Convert 1 to fraction \frac{2}{2}.

$$\frac{2}{2}-\frac{1}{2}+\frac{|-6|}{2}$$

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

$$\frac{2-1}{2}+\frac{|-6|}{2}$$

Subtract 1 from 2 to get 1.

$$\frac{1}{2}+\frac{|-6|}{2}$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -6 is 6.

$$\frac{1}{2}+\frac{6}{2}$$

Since \frac{1}{2} and \frac{6}{2} have the same denominator, add them by adding their numerators.

$$\frac{1+6}{2}$$

Add 1 and 6 to get 7.

$$\frac{7}{2}$$

Factor

$$\frac{7}{2} = 3\frac{1}{2} = 3.5$$