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

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

Evaluate

$$-\frac{508}{357}\approx -1.422969188$$

Solution Steps

Fraction \frac{-9}{7} can be rewritten as -\frac{9}{7} by extracting the negative sign.

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

Least common multiple of 12 and 7 is 84. Convert \frac{5}{12} and \frac{9}{7} to fractions with denominator 84.

$$\frac{35}{84}-\frac{108}{84}-\frac{7}{12}+|\frac{-1}{2}|+\frac{-8}{17}$$

Since \frac{35}{84} and \frac{108}{84} have the same denominator, subtract them by subtracting their numerators.

$$\frac{35-108}{84}-\frac{7}{12}+|\frac{-1}{2}|+\frac{-8}{17}$$

Subtract 108 from 35 to get -73.

$$-\frac{73}{84}-\frac{7}{12}+|\frac{-1}{2}|+\frac{-8}{17}$$

Least common multiple of 84 and 12 is 84. Convert -\frac{73}{84} and \frac{7}{12} to fractions with denominator 84.

$$-\frac{73}{84}-\frac{49}{84}+|\frac{-1}{2}|+\frac{-8}{17}$$

Since -\frac{73}{84} and \frac{49}{84} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-73-49}{84}+|\frac{-1}{2}|+\frac{-8}{17}$$

Subtract 49 from -73 to get -122.

$$\frac{-122}{84}+|\frac{-1}{2}|+\frac{-8}{17}$$

Reduce the fraction \frac{-122}{84} to lowest terms by extracting and canceling out 2.

$$-\frac{61}{42}+|\frac{-1}{2}|+\frac{-8}{17}$$

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

$$-\frac{61}{42}+|-\frac{1}{2}|+\frac{-8}{17}$$

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}.

$$-\frac{61}{42}+\frac{1}{2}+\frac{-8}{17}$$

Least common multiple of 42 and 2 is 42. Convert -\frac{61}{42} and \frac{1}{2} to fractions with denominator 42.

$$-\frac{61}{42}+\frac{21}{42}+\frac{-8}{17}$$

Since -\frac{61}{42} and \frac{21}{42} have the same denominator, add them by adding their numerators.

$$\frac{-61+21}{42}+\frac{-8}{17}$$

Add -61 and 21 to get -40.

$$\frac{-40}{42}+\frac{-8}{17}$$

Reduce the fraction \frac{-40}{42} to lowest terms by extracting and canceling out 2.

$$-\frac{20}{21}+\frac{-8}{17}$$

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

$$-\frac{20}{21}-\frac{8}{17}$$

Least common multiple of 21 and 17 is 357. Convert -\frac{20}{21} and \frac{8}{17} to fractions with denominator 357.

$$-\frac{340}{357}-\frac{168}{357}$$

Since -\frac{340}{357} and \frac{168}{357} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-340-168}{357}$$

Subtract 168 from -340 to get -508.

$$-\frac{508}{357}$$

Factor

$$-\frac{508}{357} = -1\frac{151}{357} = -1.42296918767507$$