Solve (3/5*1/3)-(1-(3/4-1/2)+frac{2}{3}-frac{3}{20})

$$( \frac { 3 } { 5 } \cdot \frac { 1 } { 3 } ) - ( 1 - ( \frac { 3 } { 4 } - \frac { 1 } { 2 } ) + \frac { 2 } { 3 } - \frac { 3 } { 20 } )$$

Evaluate

$$-\frac{16}{15}\approx -1.066666667$$

Solution Steps

Multiply \frac{3}{5} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 1}{5\times 3}-\left(1-\left(\frac{3}{4}-\frac{1}{2}\right)+\frac{2}{3}-\frac{3}{20}\right)$$

Cancel out 3 in both numerator and denominator.

$$\frac{1}{5}-\left(1-\left(\frac{3}{4}-\frac{1}{2}\right)+\frac{2}{3}-\frac{3}{20}\right)$$

Least common multiple of 4 and 2 is 4. Convert \frac{3}{4} and \frac{1}{2} to fractions with denominator 4.

$$\frac{1}{5}-\left(1-\left(\frac{3}{4}-\frac{2}{4}\right)+\frac{2}{3}-\frac{3}{20}\right)$$

Since \frac{3}{4} and \frac{2}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{5}-\left(1-\frac{3-2}{4}+\frac{2}{3}-\frac{3}{20}\right)$$

Subtract 2 from 3 to get 1.

$$\frac{1}{5}-\left(1-\frac{1}{4}+\frac{2}{3}-\frac{3}{20}\right)$$

Convert 1 to fraction \frac{4}{4}.

$$\frac{1}{5}-\left(\frac{4}{4}-\frac{1}{4}+\frac{2}{3}-\frac{3}{20}\right)$$

Since \frac{4}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{5}-\left(\frac{4-1}{4}+\frac{2}{3}-\frac{3}{20}\right)$$

Subtract 1 from 4 to get 3.

$$\frac{1}{5}-\left(\frac{3}{4}+\frac{2}{3}-\frac{3}{20}\right)$$

Least common multiple of 4 and 3 is 12. Convert \frac{3}{4} and \frac{2}{3} to fractions with denominator 12.

$$\frac{1}{5}-\left(\frac{9}{12}+\frac{8}{12}-\frac{3}{20}\right)$$

Since \frac{9}{12} and \frac{8}{12} have the same denominator, add them by adding their numerators.

$$\frac{1}{5}-\left(\frac{9+8}{12}-\frac{3}{20}\right)$$

Add 9 and 8 to get 17.

$$\frac{1}{5}-\left(\frac{17}{12}-\frac{3}{20}\right)$$

Least common multiple of 12 and 20 is 60. Convert \frac{17}{12} and \frac{3}{20} to fractions with denominator 60.

$$\frac{1}{5}-\left(\frac{85}{60}-\frac{9}{60}\right)$$

Since \frac{85}{60} and \frac{9}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{5}-\frac{85-9}{60}$$

Subtract 9 from 85 to get 76.

$$\frac{1}{5}-\frac{76}{60}$$

Reduce the fraction \frac{76}{60} to lowest terms by extracting and canceling out 4.

$$\frac{1}{5}-\frac{19}{15}$$

Least common multiple of 5 and 15 is 15. Convert \frac{1}{5} and \frac{19}{15} to fractions with denominator 15.

$$\frac{3}{15}-\frac{19}{15}$$

Since \frac{3}{15} and \frac{19}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-19}{15}$$

Subtract 19 from 3 to get -16.

$$-\frac{16}{15}$$

Factor

$$-\frac{16}{15} = -1\frac{1}{15} = -1.0666666666666667$$