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

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

Evaluate

$$-\frac{37}{20}=-1.85$$

Solution Steps

Least common multiple of 2 and 3 is 6. Convert \frac{3}{2} and \frac{1}{3} to fractions with denominator 6.

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

Since \frac{9}{6} and \frac{2}{6} have the same denominator, add them by adding their numerators.

$$\frac{9+2}{6}\times \frac{1}{2}-\frac{\frac{4}{5}}{3}-\frac{5}{2}$$

Add 9 and 2 to get 11.

$$\frac{11}{6}\times \frac{1}{2}-\frac{\frac{4}{5}}{3}-\frac{5}{2}$$

Multiply \frac{11}{6} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{11\times 1}{6\times 2}-\frac{\frac{4}{5}}{3}-\frac{5}{2}$$

Do the multiplications in the fraction \frac{11\times 1}{6\times 2}.

$$\frac{11}{12}-\frac{\frac{4}{5}}{3}-\frac{5}{2}$$

Express \frac{\frac{4}{5}}{3} as a single fraction.

$$\frac{11}{12}-\frac{4}{5\times 3}-\frac{5}{2}$$

Multiply 5 and 3 to get 15.

$$\frac{11}{12}-\frac{4}{15}-\frac{5}{2}$$

Least common multiple of 12 and 15 is 60. Convert \frac{11}{12} and \frac{4}{15} to fractions with denominator 60.

$$\frac{55}{60}-\frac{16}{60}-\frac{5}{2}$$

Since \frac{55}{60} and \frac{16}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{55-16}{60}-\frac{5}{2}$$

Subtract 16 from 55 to get 39.

$$\frac{39}{60}-\frac{5}{2}$$

Reduce the fraction \frac{39}{60} to lowest terms by extracting and canceling out 3.

$$\frac{13}{20}-\frac{5}{2}$$

Least common multiple of 20 and 2 is 20. Convert \frac{13}{20} and \frac{5}{2} to fractions with denominator 20.

$$\frac{13}{20}-\frac{50}{20}$$

Since \frac{13}{20} and \frac{50}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{13-50}{20}$$

Subtract 50 from 13 to get -37.

$$-\frac{37}{20}$$

Factor

$$-\frac{37}{20} = -1\frac{17}{20} = -1.85$$