Solve (1/5+1/5)-(4/3+3/4)

$$( \frac { 1 } { 5 } + \frac { 1 } { 5 } ) - ( \frac { 4 } { 3 } + \frac { 3 } { 4 } )$$

Evaluate

$$-\frac{101}{60}\approx -1.683333333$$

Solution Steps

Since \frac{1}{5} and \frac{1}{5} have the same denominator, add them by adding their numerators.

$$\frac{1+1}{5}-\left(\frac{4}{3}+\frac{3}{4}\right)$$

Add 1 and 1 to get 2.

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

Least common multiple of 3 and 4 is 12. Convert \frac{4}{3} and \frac{3}{4} to fractions with denominator 12.

$$\frac{2}{5}-\left(\frac{16}{12}+\frac{9}{12}\right)$$

Since \frac{16}{12} and \frac{9}{12} have the same denominator, add them by adding their numerators.

$$\frac{2}{5}-\frac{16+9}{12}$$

Add 16 and 9 to get 25.

$$\frac{2}{5}-\frac{25}{12}$$

Least common multiple of 5 and 12 is 60. Convert \frac{2}{5} and \frac{25}{12} to fractions with denominator 60.

$$\frac{24}{60}-\frac{125}{60}$$

Since \frac{24}{60} and \frac{125}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{24-125}{60}$$

Subtract 125 from 24 to get -101.

$$-\frac{101}{60}$$

Factor

$$-\frac{101}{60} = -1\frac{41}{60} = -1.6833333333333333$$