Solve 7/2+[5/4-8-9/3-(23/2+frac{7}{5})]

$$\frac { 7 } { 2 } + [ \frac { 5 } { 4 } - 8 - \frac { 9 } { 3 } - ( \frac { 23 } { 2 } + \frac { 7 } { 5 } ) ]$$

Evaluate

$$-\frac{383}{20}=-19.15$$

Solution Steps

Convert 8 to fraction \frac{32}{4}.

$$\frac{7}{2}+\frac{5}{4}-\frac{32}{4}-\frac{9}{3}-\left(\frac{23}{2}+\frac{7}{5}\right)$$

Since \frac{5}{4} and \frac{32}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7}{2}+\frac{5-32}{4}-\frac{9}{3}-\left(\frac{23}{2}+\frac{7}{5}\right)$$

Subtract 32 from 5 to get -27.

$$\frac{7}{2}+-\frac{27}{4}-\frac{9}{3}-\left(\frac{23}{2}+\frac{7}{5}\right)$$

Divide 9 by 3 to get 3.

$$\frac{7}{2}+-\frac{27}{4}-3-\left(\frac{23}{2}+\frac{7}{5}\right)$$

Convert 3 to fraction \frac{12}{4}.

$$\frac{7}{2}+-\frac{27}{4}-\frac{12}{4}-\left(\frac{23}{2}+\frac{7}{5}\right)$$

Since -\frac{27}{4} and \frac{12}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7}{2}+\frac{-27-12}{4}-\left(\frac{23}{2}+\frac{7}{5}\right)$$

Subtract 12 from -27 to get -39.

$$\frac{7}{2}+-\frac{39}{4}-\left(\frac{23}{2}+\frac{7}{5}\right)$$

Least common multiple of 2 and 5 is 10. Convert \frac{23}{2} and \frac{7}{5} to fractions with denominator 10.

$$\frac{7}{2}+-\frac{39}{4}-\left(\frac{115}{10}+\frac{14}{10}\right)$$

Since \frac{115}{10} and \frac{14}{10} have the same denominator, add them by adding their numerators.

$$\frac{7}{2}-\frac{39}{4}-\frac{115+14}{10}$$

Add 115 and 14 to get 129.

$$\frac{7}{2}-\frac{39}{4}-\frac{129}{10}$$

Least common multiple of 4 and 10 is 20. Convert -\frac{39}{4} and \frac{129}{10} to fractions with denominator 20.

$$\frac{7}{2}-\frac{195}{20}-\frac{258}{20}$$

Since -\frac{195}{20} and \frac{258}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7}{2}+\frac{-195-258}{20}$$

Subtract 258 from -195 to get -453.

$$\frac{7}{2}-\frac{453}{20}$$

Least common multiple of 2 and 20 is 20. Convert \frac{7}{2} and \frac{453}{20} to fractions with denominator 20.

$$\frac{70}{20}-\frac{453}{20}$$

Since \frac{70}{20} and \frac{453}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{70-453}{20}$$

Subtract 453 from 70 to get -383.

$$-\frac{383}{20}$$

Factor

$$-\frac{383}{20} = -19\frac{3}{20} = -19.15$$