Solve 5{3-[(-5/2+3/5+1/4)*(-6/11)]}*(1-frac{3}{4}-frac{7}{3})

$$5 \{ 3 - [ ( - \frac { 5 } { 2 } + \frac { 3 } { 5 } + \frac { 1 } { 4 } ) \cdot ( - \frac { 6 } { 11 } ) ] \} \cdot ( 1 - \frac { 3 } { 4 } - \frac { 7 } { 3 } )$$

Evaluate

$$-\frac{175}{8}=-21.875$$

Solution Steps

Least common multiple of 2 and 5 is 10. Convert -\frac{5}{2} and \frac{3}{5} to fractions with denominator 10.

$$5\left(3-\left(-\frac{25}{10}+\frac{6}{10}+\frac{1}{4}\right)\left(-\frac{6}{11}\right)\right)\left(1-\frac{3}{4}-\frac{7}{3}\right)$$

Since -\frac{25}{10} and \frac{6}{10} have the same denominator, add them by adding their numerators.

$$5\left(3-\left(\frac{-25+6}{10}+\frac{1}{4}\right)\left(-\frac{6}{11}\right)\right)\left(1-\frac{3}{4}-\frac{7}{3}\right)$$

Add -25 and 6 to get -19.

$$5\left(3-\left(-\frac{19}{10}+\frac{1}{4}\right)\left(-\frac{6}{11}\right)\right)\left(1-\frac{3}{4}-\frac{7}{3}\right)$$

Least common multiple of 10 and 4 is 20. Convert -\frac{19}{10} and \frac{1}{4} to fractions with denominator 20.

$$5\left(3-\left(-\frac{38}{20}+\frac{5}{20}\right)\left(-\frac{6}{11}\right)\right)\left(1-\frac{3}{4}-\frac{7}{3}\right)$$

Since -\frac{38}{20} and \frac{5}{20} have the same denominator, add them by adding their numerators.

$$5\left(3-\frac{-38+5}{20}\left(-\frac{6}{11}\right)\right)\left(1-\frac{3}{4}-\frac{7}{3}\right)$$

Add -38 and 5 to get -33.

$$5\left(3-\left(-\frac{33}{20}\left(-\frac{6}{11}\right)\right)\right)\left(1-\frac{3}{4}-\frac{7}{3}\right)$$

Multiply -\frac{33}{20} times -\frac{6}{11} by multiplying numerator times numerator and denominator times denominator.

$$5\left(3-\frac{-33\left(-6\right)}{20\times 11}\right)\left(1-\frac{3}{4}-\frac{7}{3}\right)$$

Do the multiplications in the fraction \frac{-33\left(-6\right)}{20\times 11}.

$$5\left(3-\frac{198}{220}\right)\left(1-\frac{3}{4}-\frac{7}{3}\right)$$

Reduce the fraction \frac{198}{220} to lowest terms by extracting and canceling out 22.

$$5\left(3-\frac{9}{10}\right)\left(1-\frac{3}{4}-\frac{7}{3}\right)$$

Convert 3 to fraction \frac{30}{10}.

$$5\left(\frac{30}{10}-\frac{9}{10}\right)\left(1-\frac{3}{4}-\frac{7}{3}\right)$$

Since \frac{30}{10} and \frac{9}{10} have the same denominator, subtract them by subtracting their numerators.

$$5\times \frac{30-9}{10}\left(1-\frac{3}{4}-\frac{7}{3}\right)$$

Subtract 9 from 30 to get 21.

$$5\times \frac{21}{10}\left(1-\frac{3}{4}-\frac{7}{3}\right)$$

Express 5\times \frac{21}{10} as a single fraction.

$$\frac{5\times 21}{10}\left(1-\frac{3}{4}-\frac{7}{3}\right)$$

Multiply 5 and 21 to get 105.

$$\frac{105}{10}\left(1-\frac{3}{4}-\frac{7}{3}\right)$$

Reduce the fraction \frac{105}{10} to lowest terms by extracting and canceling out 5.

$$\frac{21}{2}\left(1-\frac{3}{4}-\frac{7}{3}\right)$$

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

$$\frac{21}{2}\left(\frac{4}{4}-\frac{3}{4}-\frac{7}{3}\right)$$

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

$$\frac{21}{2}\left(\frac{4-3}{4}-\frac{7}{3}\right)$$

Subtract 3 from 4 to get 1.

$$\frac{21}{2}\left(\frac{1}{4}-\frac{7}{3}\right)$$

Least common multiple of 4 and 3 is 12. Convert \frac{1}{4} and \frac{7}{3} to fractions with denominator 12.

$$\frac{21}{2}\left(\frac{3}{12}-\frac{28}{12}\right)$$

Since \frac{3}{12} and \frac{28}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{21}{2}\times \frac{3-28}{12}$$

Subtract 28 from 3 to get -25.

$$\frac{21}{2}\left(-\frac{25}{12}\right)$$

Multiply \frac{21}{2} times -\frac{25}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{21\left(-25\right)}{2\times 12}$$

Do the multiplications in the fraction \frac{21\left(-25\right)}{2\times 12}.

$$\frac{-525}{24}$$

Reduce the fraction \frac{-525}{24} to lowest terms by extracting and canceling out 3.

$$-\frac{175}{8}$$

Factor

$$-\frac{175}{8} = -21\frac{7}{8} = -21.875$$