Solve 5/12+-9/17--7/12+|-1/2|+frac{-8}{17}

$$\frac { 5 } { 12 } + \frac { - 9 } { 17 } - \frac { - 7 } { 12 } + | \frac { - 1 } { 2 } | + \frac { - 8 } { 17 }$$

Evaluate

$$\frac{1}{2}=0.5$$

Solution Steps

Fraction \frac{-9}{17} can be rewritten as -\frac{9}{17} by extracting the negative sign.

$$\frac{5}{12}-\frac{9}{17}-\frac{-7}{12}+|\frac{-1}{2}|+\frac{-8}{17}$$

Least common multiple of 12 and 17 is 204. Convert \frac{5}{12} and \frac{9}{17} to fractions with denominator 204.

$$\frac{85}{204}-\frac{108}{204}-\frac{-7}{12}+|\frac{-1}{2}|+\frac{-8}{17}$$

Since \frac{85}{204} and \frac{108}{204} have the same denominator, subtract them by subtracting their numerators.

$$\frac{85-108}{204}-\frac{-7}{12}+|\frac{-1}{2}|+\frac{-8}{17}$$

Subtract 108 from 85 to get -23.

$$-\frac{23}{204}-\frac{-7}{12}+|\frac{-1}{2}|+\frac{-8}{17}$$

Fraction \frac{-7}{12} can be rewritten as -\frac{7}{12} by extracting the negative sign.

$$-\frac{23}{204}-\left(-\frac{7}{12}\right)+|\frac{-1}{2}|+\frac{-8}{17}$$

The opposite of -\frac{7}{12} is \frac{7}{12}.

$$-\frac{23}{204}+\frac{7}{12}+|\frac{-1}{2}|+\frac{-8}{17}$$

Least common multiple of 204 and 12 is 204. Convert -\frac{23}{204} and \frac{7}{12} to fractions with denominator 204.

$$-\frac{23}{204}+\frac{119}{204}+|\frac{-1}{2}|+\frac{-8}{17}$$

Since -\frac{23}{204} and \frac{119}{204} have the same denominator, add them by adding their numerators.

$$\frac{-23+119}{204}+|\frac{-1}{2}|+\frac{-8}{17}$$

Add -23 and 119 to get 96.

$$\frac{96}{204}+|\frac{-1}{2}|+\frac{-8}{17}$$

Reduce the fraction \frac{96}{204} to lowest terms by extracting and canceling out 12.

$$\frac{8}{17}+|\frac{-1}{2}|+\frac{-8}{17}$$

Fraction \frac{-1}{2} can be rewritten as -\frac{1}{2} by extracting the negative sign.

$$\frac{8}{17}+|-\frac{1}{2}|+\frac{-8}{17}$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{1}{2} is \frac{1}{2}.

$$\frac{8}{17}+\frac{1}{2}+\frac{-8}{17}$$

Least common multiple of 17 and 2 is 34. Convert \frac{8}{17} and \frac{1}{2} to fractions with denominator 34.

$$\frac{16}{34}+\frac{17}{34}+\frac{-8}{17}$$

Since \frac{16}{34} and \frac{17}{34} have the same denominator, add them by adding their numerators.

$$\frac{16+17}{34}+\frac{-8}{17}$$

Add 16 and 17 to get 33.

$$\frac{33}{34}+\frac{-8}{17}$$

Fraction \frac{-8}{17} can be rewritten as -\frac{8}{17} by extracting the negative sign.

$$\frac{33}{34}-\frac{8}{17}$$

Least common multiple of 34 and 17 is 34. Convert \frac{33}{34} and \frac{8}{17} to fractions with denominator 34.

$$\frac{33}{34}-\frac{16}{34}$$

Since \frac{33}{34} and \frac{16}{34} have the same denominator, subtract them by subtracting their numerators.

$$\frac{33-16}{34}$$

Subtract 16 from 33 to get 17.

$$\frac{17}{34}$$

Reduce the fraction \frac{17}{34} to lowest terms by extracting and canceling out 17.

$$\frac{1}{2}$$

Factor

$$\frac{1}{2} = 0.5$$