Solve -{-2/5-3(5/20+4/10)+[5/2+2(frac{1}{8}-frac{3}{4})]}frac{3}{4}

$$- \{ - \frac { 2 } { 5 } - 3 ( \frac { 5 } { 20 } + \frac { 4 } { 10 } ) + [ \frac { 5 } { 2 } + 2 ( \frac { 1 } { 8 } - \frac { 3 } { 4 } ) ] \} \frac { 3 } { 4 }$$

Evaluate

$$\frac{33}{40}=0.825$$

Solution Steps

Reduce the fraction \frac{5}{20} to lowest terms by extracting and canceling out 5.

$$\left(-\left(-\frac{2}{5}-3\left(\frac{1}{4}+\frac{4}{10}\right)+\frac{5}{2}+2\left(\frac{1}{8}-\frac{3}{4}\right)\right)\right)\times \frac{3}{4}$$

Reduce the fraction \frac{4}{10} to lowest terms by extracting and canceling out 2.

$$\left(-\left(-\frac{2}{5}-3\left(\frac{1}{4}+\frac{2}{5}\right)+\frac{5}{2}+2\left(\frac{1}{8}-\frac{3}{4}\right)\right)\right)\times \frac{3}{4}$$

Least common multiple of 4 and 5 is 20. Convert \frac{1}{4} and \frac{2}{5} to fractions with denominator 20.

$$\left(-\left(-\frac{2}{5}-3\left(\frac{5}{20}+\frac{8}{20}\right)+\frac{5}{2}+2\left(\frac{1}{8}-\frac{3}{4}\right)\right)\right)\times \frac{3}{4}$$

Since \frac{5}{20} and \frac{8}{20} have the same denominator, add them by adding their numerators.

$$\left(-\left(-\frac{2}{5}-3\times \frac{5+8}{20}+\frac{5}{2}+2\left(\frac{1}{8}-\frac{3}{4}\right)\right)\right)\times \frac{3}{4}$$

Add 5 and 8 to get 13.

$$\left(-\left(-\frac{2}{5}-3\times \frac{13}{20}+\frac{5}{2}+2\left(\frac{1}{8}-\frac{3}{4}\right)\right)\right)\times \frac{3}{4}$$

Express 3\times \frac{13}{20} as a single fraction.

$$\left(-\left(-\frac{2}{5}-\frac{3\times 13}{20}+\frac{5}{2}+2\left(\frac{1}{8}-\frac{3}{4}\right)\right)\right)\times \frac{3}{4}$$

Multiply 3 and 13 to get 39.

$$\left(-\left(-\frac{2}{5}-\frac{39}{20}+\frac{5}{2}+2\left(\frac{1}{8}-\frac{3}{4}\right)\right)\right)\times \frac{3}{4}$$

Least common multiple of 5 and 20 is 20. Convert -\frac{2}{5} and \frac{39}{20} to fractions with denominator 20.

$$\left(-\left(-\frac{8}{20}-\frac{39}{20}+\frac{5}{2}+2\left(\frac{1}{8}-\frac{3}{4}\right)\right)\right)\times \frac{3}{4}$$

Since -\frac{8}{20} and \frac{39}{20} have the same denominator, subtract them by subtracting their numerators.

$$\left(-\left(\frac{-8-39}{20}+\frac{5}{2}+2\left(\frac{1}{8}-\frac{3}{4}\right)\right)\right)\times \frac{3}{4}$$

Subtract 39 from -8 to get -47.

$$\left(-\left(-\frac{47}{20}+\frac{5}{2}+2\left(\frac{1}{8}-\frac{3}{4}\right)\right)\right)\times \frac{3}{4}$$

Least common multiple of 20 and 2 is 20. Convert -\frac{47}{20} and \frac{5}{2} to fractions with denominator 20.

$$\left(-\left(-\frac{47}{20}+\frac{50}{20}+2\left(\frac{1}{8}-\frac{3}{4}\right)\right)\right)\times \frac{3}{4}$$

Since -\frac{47}{20} and \frac{50}{20} have the same denominator, add them by adding their numerators.

$$\left(-\left(\frac{-47+50}{20}+2\left(\frac{1}{8}-\frac{3}{4}\right)\right)\right)\times \frac{3}{4}$$

Add -47 and 50 to get 3.

$$\left(-\left(\frac{3}{20}+2\left(\frac{1}{8}-\frac{3}{4}\right)\right)\right)\times \frac{3}{4}$$

Least common multiple of 8 and 4 is 8. Convert \frac{1}{8} and \frac{3}{4} to fractions with denominator 8.

$$\left(-\left(\frac{3}{20}+2\left(\frac{1}{8}-\frac{6}{8}\right)\right)\right)\times \frac{3}{4}$$

Since \frac{1}{8} and \frac{6}{8} have the same denominator, subtract them by subtracting their numerators.

$$\left(-\left(\frac{3}{20}+2\times \frac{1-6}{8}\right)\right)\times \frac{3}{4}$$

Subtract 6 from 1 to get -5.

$$\left(-\left(\frac{3}{20}+2\left(-\frac{5}{8}\right)\right)\right)\times \frac{3}{4}$$

Express 2\left(-\frac{5}{8}\right) as a single fraction.

$$\left(-\left(\frac{3}{20}+\frac{2\left(-5\right)}{8}\right)\right)\times \frac{3}{4}$$

Multiply 2 and -5 to get -10.

$$\left(-\left(\frac{3}{20}+\frac{-10}{8}\right)\right)\times \frac{3}{4}$$

Reduce the fraction \frac{-10}{8} to lowest terms by extracting and canceling out 2.

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

Least common multiple of 20 and 4 is 20. Convert \frac{3}{20} and \frac{5}{4} to fractions with denominator 20.

$$\left(-\left(\frac{3}{20}-\frac{25}{20}\right)\right)\times \frac{3}{4}$$

Since \frac{3}{20} and \frac{25}{20} have the same denominator, subtract them by subtracting their numerators.

$$\left(-\frac{3-25}{20}\right)\times \frac{3}{4}$$

Subtract 25 from 3 to get -22.

$$\left(-\frac{-22}{20}\right)\times \frac{3}{4}$$

Reduce the fraction \frac{-22}{20} to lowest terms by extracting and canceling out 2.

$$\left(-\left(-\frac{11}{10}\right)\right)\times \frac{3}{4}$$

The opposite of -\frac{11}{10} is \frac{11}{10}.

$$\frac{11}{10}\times \frac{3}{4}$$

Multiply \frac{11}{10} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{11\times 3}{10\times 4}$$

Do the multiplications in the fraction \frac{11\times 3}{10\times 4}.

$$\frac{33}{40}$$

Factor

$$\frac{3 \cdot 11}{2 ^ {3} \cdot 5} = 0.825$$