Solve -5/4+7/6-3/9+5/8-frac{4}{2}

$$- \frac { 5 } { 4 } + \frac { 7 } { 6 } - \frac { 3 } { 9 } + \frac { 5 } { 8 } - \frac { 4 } { 2 }$$

Evaluate

$$-\frac{43}{24}\approx -1.791666667$$

Solution Steps

Least common multiple of 4 and 6 is 12. Convert -\frac{5}{4} and \frac{7}{6} to fractions with denominator 12.

$$-\frac{15}{12}+\frac{14}{12}-\frac{3}{9}+\frac{5}{8}-\frac{4}{2}$$

Since -\frac{15}{12} and \frac{14}{12} have the same denominator, add them by adding their numerators.

$$\frac{-15+14}{12}-\frac{3}{9}+\frac{5}{8}-\frac{4}{2}$$

Add -15 and 14 to get -1.

$$-\frac{1}{12}-\frac{3}{9}+\frac{5}{8}-\frac{4}{2}$$

Reduce the fraction \frac{3}{9} to lowest terms by extracting and canceling out 3.

$$-\frac{1}{12}-\frac{1}{3}+\frac{5}{8}-\frac{4}{2}$$

Least common multiple of 12 and 3 is 12. Convert -\frac{1}{12} and \frac{1}{3} to fractions with denominator 12.

$$-\frac{1}{12}-\frac{4}{12}+\frac{5}{8}-\frac{4}{2}$$

Since -\frac{1}{12} and \frac{4}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-1-4}{12}+\frac{5}{8}-\frac{4}{2}$$

Subtract 4 from -1 to get -5.

$$-\frac{5}{12}+\frac{5}{8}-\frac{4}{2}$$

Least common multiple of 12 and 8 is 24. Convert -\frac{5}{12} and \frac{5}{8} to fractions with denominator 24.

$$-\frac{10}{24}+\frac{15}{24}-\frac{4}{2}$$

Since -\frac{10}{24} and \frac{15}{24} have the same denominator, add them by adding their numerators.

$$\frac{-10+15}{24}-\frac{4}{2}$$

Add -10 and 15 to get 5.

$$\frac{5}{24}-\frac{4}{2}$$

Divide 4 by 2 to get 2.

$$\frac{5}{24}-2$$

Convert 2 to fraction \frac{48}{24}.

$$\frac{5}{24}-\frac{48}{24}$$

Since \frac{5}{24} and \frac{48}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5-48}{24}$$

Subtract 48 from 5 to get -43.

$$-\frac{43}{24}$$

Factor

$$-\frac{43}{24} = -1\frac{19}{24} = -1.7916666666666667$$