Solve 5:1/2+(-1)^2007+sqrt{1/4}-|-5|

$$5 : \frac { 1 } { 2 } + ( - 1 ) ^ { 2007 } + \sqrt { \frac { 1 } { 4 } } - | - 5 |$$

Evaluate

$$\frac{9}{2}=4.5$$

Solution Steps

Divide 5 by \frac{1}{2} by multiplying 5 by the reciprocal of \frac{1}{2}.

$$5\times 2+\left(-1\right)^{2007}+\sqrt{\frac{1}{4}}-|-5|$$

Multiply 5 and 2 to get 10.

$$10+\left(-1\right)^{2007}+\sqrt{\frac{1}{4}}-|-5|$$

Calculate -1 to the power of 2007 and get -1.

$$10-1+\sqrt{\frac{1}{4}}-|-5|$$

Subtract 1 from 10 to get 9.

$$9+\sqrt{\frac{1}{4}}-|-5|$$

Rewrite the square root of the division \frac{1}{4} as the division of square roots \frac{\sqrt{1}}{\sqrt{4}}. Take the square root of both numerator and denominator.

$$9+\frac{1}{2}-|-5|$$

Convert 9 to fraction \frac{18}{2}.

$$\frac{18}{2}+\frac{1}{2}-|-5|$$

Since \frac{18}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$\frac{18+1}{2}-|-5|$$

Add 18 and 1 to get 19.

$$\frac{19}{2}-|-5|$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -5 is 5.

$$\frac{19}{2}-5$$

Convert 5 to fraction \frac{10}{2}.

$$\frac{19}{2}-\frac{10}{2}$$

Since \frac{19}{2} and \frac{10}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{19-10}{2}$$

Subtract 10 from 19 to get 9.

$$\frac{9}{2}$$

Factor

$$\frac{3 ^ {2}}{2} = 4\frac{1}{2} = 4.5$$