Solve 4/11-1:3/2+4/9(-2)+4/3:(-1)-[frac{5}{18}-frac{2}{3})frac{3}{2}=

$$\frac { 4 } { 11 } - 1 : \frac { 3 } { 2 } + \frac { 4 } { 9 } ( - 2 ) + \frac { 4 } { 3 } : ( - 1 ) - [ \frac { 5 } { 18 } - \frac { 2 } { 3 } ) \frac { 3 } { 2 } =$$

Evaluate

$$-\frac{769}{396}\approx -1.941919192$$

Solution Steps

Divide 1 by \frac{3}{2} by multiplying 1 by the reciprocal of \frac{3}{2}.

$$\frac{4}{11}-1\times \frac{2}{3}+\frac{4}{9}\left(-2\right)+\frac{\frac{4}{3}}{-1}-\left(\frac{5}{18}-\frac{2}{3}\right)\times \frac{3}{2}$$

Multiply 1 and \frac{2}{3} to get \frac{2}{3}.

$$\frac{4}{11}-\frac{2}{3}+\frac{4}{9}\left(-2\right)+\frac{\frac{4}{3}}{-1}-\left(\frac{5}{18}-\frac{2}{3}\right)\times \frac{3}{2}$$

Least common multiple of 11 and 3 is 33. Convert \frac{4}{11} and \frac{2}{3} to fractions with denominator 33.

$$\frac{12}{33}-\frac{22}{33}+\frac{4}{9}\left(-2\right)+\frac{\frac{4}{3}}{-1}-\left(\frac{5}{18}-\frac{2}{3}\right)\times \frac{3}{2}$$

Since \frac{12}{33} and \frac{22}{33} have the same denominator, subtract them by subtracting their numerators.

$$\frac{12-22}{33}+\frac{4}{9}\left(-2\right)+\frac{\frac{4}{3}}{-1}-\left(\frac{5}{18}-\frac{2}{3}\right)\times \frac{3}{2}$$

Subtract 22 from 12 to get -10.

$$-\frac{10}{33}+\frac{4}{9}\left(-2\right)+\frac{\frac{4}{3}}{-1}-\left(\frac{5}{18}-\frac{2}{3}\right)\times \frac{3}{2}$$

Express \frac{4}{9}\left(-2\right) as a single fraction.

$$-\frac{10}{33}+\frac{4\left(-2\right)}{9}+\frac{\frac{4}{3}}{-1}-\left(\frac{5}{18}-\frac{2}{3}\right)\times \frac{3}{2}$$

Multiply 4 and -2 to get -8.

$$-\frac{10}{33}+\frac{-8}{9}+\frac{\frac{4}{3}}{-1}-\left(\frac{5}{18}-\frac{2}{3}\right)\times \frac{3}{2}$$

Fraction \frac{-8}{9} can be rewritten as -\frac{8}{9} by extracting the negative sign.

$$-\frac{10}{33}-\frac{8}{9}+\frac{\frac{4}{3}}{-1}-\left(\frac{5}{18}-\frac{2}{3}\right)\times \frac{3}{2}$$

Least common multiple of 33 and 9 is 99. Convert -\frac{10}{33} and \frac{8}{9} to fractions with denominator 99.

$$-\frac{30}{99}-\frac{88}{99}+\frac{\frac{4}{3}}{-1}-\left(\frac{5}{18}-\frac{2}{3}\right)\times \frac{3}{2}$$

Since -\frac{30}{99} and \frac{88}{99} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-30-88}{99}+\frac{\frac{4}{3}}{-1}-\left(\frac{5}{18}-\frac{2}{3}\right)\times \frac{3}{2}$$

Subtract 88 from -30 to get -118.

$$-\frac{118}{99}+\frac{\frac{4}{3}}{-1}-\left(\frac{5}{18}-\frac{2}{3}\right)\times \frac{3}{2}$$

Express \frac{\frac{4}{3}}{-1} as a single fraction.

$$-\frac{118}{99}+\frac{4}{3\left(-1\right)}-\left(\frac{5}{18}-\frac{2}{3}\right)\times \frac{3}{2}$$

Multiply 3 and -1 to get -3.

$$-\frac{118}{99}+\frac{4}{-3}-\left(\frac{5}{18}-\frac{2}{3}\right)\times \frac{3}{2}$$

Fraction \frac{4}{-3} can be rewritten as -\frac{4}{3} by extracting the negative sign.

$$-\frac{118}{99}-\frac{4}{3}-\left(\frac{5}{18}-\frac{2}{3}\right)\times \frac{3}{2}$$

Least common multiple of 99 and 3 is 99. Convert -\frac{118}{99} and \frac{4}{3} to fractions with denominator 99.

$$-\frac{118}{99}-\frac{132}{99}-\left(\frac{5}{18}-\frac{2}{3}\right)\times \frac{3}{2}$$

Since -\frac{118}{99} and \frac{132}{99} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-118-132}{99}-\left(\frac{5}{18}-\frac{2}{3}\right)\times \frac{3}{2}$$

Subtract 132 from -118 to get -250.

$$-\frac{250}{99}-\left(\frac{5}{18}-\frac{2}{3}\right)\times \frac{3}{2}$$

Least common multiple of 18 and 3 is 18. Convert \frac{5}{18} and \frac{2}{3} to fractions with denominator 18.

$$-\frac{250}{99}-\left(\frac{5}{18}-\frac{12}{18}\right)\times \frac{3}{2}$$

Since \frac{5}{18} and \frac{12}{18} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{250}{99}-\frac{5-12}{18}\times \frac{3}{2}$$

Subtract 12 from 5 to get -7.

$$-\frac{250}{99}-\left(-\frac{7}{18}\times \frac{3}{2}\right)$$

Multiply -\frac{7}{18} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{250}{99}-\frac{-7\times 3}{18\times 2}$$

Do the multiplications in the fraction \frac{-7\times 3}{18\times 2}.

$$-\frac{250}{99}-\frac{-21}{36}$$

Reduce the fraction \frac{-21}{36} to lowest terms by extracting and canceling out 3.

$$-\frac{250}{99}-\left(-\frac{7}{12}\right)$$

The opposite of -\frac{7}{12} is \frac{7}{12}.

$$-\frac{250}{99}+\frac{7}{12}$$

Least common multiple of 99 and 12 is 396. Convert -\frac{250}{99} and \frac{7}{12} to fractions with denominator 396.

$$-\frac{1000}{396}+\frac{231}{396}$$

Since -\frac{1000}{396} and \frac{231}{396} have the same denominator, add them by adding their numerators.

$$\frac{-1000+231}{396}$$

Add -1000 and 231 to get -769.

$$-\frac{769}{396}$$

Factor

$$-\frac{769}{396} = -1\frac{373}{396} = -1.9419191919191918$$