Solve (4/3-5/4-1/2)-(3/5-frac{4}{9}+frac{5}{2}

$$( \frac { 4 } { 3 } - \frac { 5 } { 4 } - \frac { 1 } { 2 } ) - ( \frac { 3 } { 5 } - \frac { 4 } { 9 } + \frac { 5 } { 2 }$$

Evaluate

$$-\frac{553}{180}\approx -3.072222222$$

Solution Steps

Least common multiple of 3 and 4 is 12. Convert \frac{4}{3} and \frac{5}{4} to fractions with denominator 12.

$$\frac{16}{12}-\frac{15}{12}-\frac{1}{2}-\left(\frac{3}{5}-\frac{4}{9}+\frac{5}{2}\right)$$

Since \frac{16}{12} and \frac{15}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{16-15}{12}-\frac{1}{2}-\left(\frac{3}{5}-\frac{4}{9}+\frac{5}{2}\right)$$

Subtract 15 from 16 to get 1.

$$\frac{1}{12}-\frac{1}{2}-\left(\frac{3}{5}-\frac{4}{9}+\frac{5}{2}\right)$$

Least common multiple of 12 and 2 is 12. Convert \frac{1}{12} and \frac{1}{2} to fractions with denominator 12.

$$\frac{1}{12}-\frac{6}{12}-\left(\frac{3}{5}-\frac{4}{9}+\frac{5}{2}\right)$$

Since \frac{1}{12} and \frac{6}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1-6}{12}-\left(\frac{3}{5}-\frac{4}{9}+\frac{5}{2}\right)$$

Subtract 6 from 1 to get -5.

$$-\frac{5}{12}-\left(\frac{3}{5}-\frac{4}{9}+\frac{5}{2}\right)$$

Least common multiple of 5 and 9 is 45. Convert \frac{3}{5} and \frac{4}{9} to fractions with denominator 45.

$$-\frac{5}{12}-\left(\frac{27}{45}-\frac{20}{45}+\frac{5}{2}\right)$$

Since \frac{27}{45} and \frac{20}{45} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{5}{12}-\left(\frac{27-20}{45}+\frac{5}{2}\right)$$

Subtract 20 from 27 to get 7.

$$-\frac{5}{12}-\left(\frac{7}{45}+\frac{5}{2}\right)$$

Least common multiple of 45 and 2 is 90. Convert \frac{7}{45} and \frac{5}{2} to fractions with denominator 90.

$$-\frac{5}{12}-\left(\frac{14}{90}+\frac{225}{90}\right)$$

Since \frac{14}{90} and \frac{225}{90} have the same denominator, add them by adding their numerators.

$$-\frac{5}{12}-\frac{14+225}{90}$$

Add 14 and 225 to get 239.

$$-\frac{5}{12}-\frac{239}{90}$$

Least common multiple of 12 and 90 is 180. Convert -\frac{5}{12} and \frac{239}{90} to fractions with denominator 180.

$$-\frac{75}{180}-\frac{478}{180}$$

Since -\frac{75}{180} and \frac{478}{180} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-75-478}{180}$$

Subtract 478 from -75 to get -553.

$$-\frac{553}{180}$$

Factor

$$-\frac{553}{180} = -3\frac{13}{180} = -3.0722222222222224$$