Solve (-3/2-4/5)+(7/3+5/2)

$$( \frac { - 3 } { 2 } - \frac { 4 } { 5 } ) + ( \frac { 7 } { 3 } + \frac { 5 } { 2 } )$$

Evaluate

$$\frac{38}{15}\approx 2.533333333$$

Solution Steps

Fraction \frac{-3}{2} can be rewritten as -\frac{3}{2} by extracting the negative sign.

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

Least common multiple of 2 and 5 is 10. Convert -\frac{3}{2} and \frac{4}{5} to fractions with denominator 10.

$$-\frac{15}{10}-\frac{8}{10}+\frac{7}{3}+\frac{5}{2}$$

Since -\frac{15}{10} and \frac{8}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-15-8}{10}+\frac{7}{3}+\frac{5}{2}$$

Subtract 8 from -15 to get -23.

$$-\frac{23}{10}+\frac{7}{3}+\frac{5}{2}$$

Least common multiple of 10 and 3 is 30. Convert -\frac{23}{10} and \frac{7}{3} to fractions with denominator 30.

$$-\frac{69}{30}+\frac{70}{30}+\frac{5}{2}$$

Since -\frac{69}{30} and \frac{70}{30} have the same denominator, add them by adding their numerators.

$$\frac{-69+70}{30}+\frac{5}{2}$$

Add -69 and 70 to get 1.

$$\frac{1}{30}+\frac{5}{2}$$

Least common multiple of 30 and 2 is 30. Convert \frac{1}{30} and \frac{5}{2} to fractions with denominator 30.

$$\frac{1}{30}+\frac{75}{30}$$

Since \frac{1}{30} and \frac{75}{30} have the same denominator, add them by adding their numerators.

$$\frac{1+75}{30}$$

Add 1 and 75 to get 76.

$$\frac{76}{30}$$

Reduce the fraction \frac{76}{30} to lowest terms by extracting and canceling out 2.

$$\frac{38}{15}$$

Factor

$$\frac{2 \cdot 19}{3 \cdot 5} = 2\frac{8}{15} = 2.533333333333333$$