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

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

Evaluate

$$-2$$

Solution Steps

Divide \frac{1}{9} by \frac{4}{11} by multiplying \frac{1}{9} by the reciprocal of \frac{4}{11}.

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

Multiply \frac{1}{9} times \frac{11}{4} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{1\times 11}{9\times 4}.

$$\frac{11}{36}-\frac{1}{\frac{3}{2}}+\frac{4}{9}\left(-2\right)+\frac{\frac{4}{3}}{-1}-\left(\frac{5}{18}-\frac{2}{3}\right)\times \frac{3}{2}$$

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

$$\frac{11}{36}-1\times \frac{2}{3}+\frac{4}{9}\left(-2\right)+\frac{\frac{4}{3}}{-1}-\left(\frac{5}{18}-\frac{2}{3}\right)\times \frac{3}{2}$$

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

$$\frac{11}{36}-\frac{2}{3}+\frac{4}{9}\left(-2\right)+\frac{\frac{4}{3}}{-1}-\left(\frac{5}{18}-\frac{2}{3}\right)\times \frac{3}{2}$$

Least common multiple of 36 and 3 is 36. Convert \frac{11}{36} and \frac{2}{3} to fractions with denominator 36.

$$\frac{11}{36}-\frac{24}{36}+\frac{4}{9}\left(-2\right)+\frac{\frac{4}{3}}{-1}-\left(\frac{5}{18}-\frac{2}{3}\right)\times \frac{3}{2}$$

Since \frac{11}{36} and \frac{24}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{11-24}{36}+\frac{4}{9}\left(-2\right)+\frac{\frac{4}{3}}{-1}-\left(\frac{5}{18}-\frac{2}{3}\right)\times \frac{3}{2}$$

Subtract 24 from 11 to get -13.

$$-\frac{13}{36}+\frac{4}{9}\left(-2\right)+\frac{\frac{4}{3}}{-1}-\left(\frac{5}{18}-\frac{2}{3}\right)\times \frac{3}{2}$$

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

$$-\frac{13}{36}+\frac{4\left(-2\right)}{9}+\frac{\frac{4}{3}}{-1}-\left(\frac{5}{18}-\frac{2}{3}\right)\times \frac{3}{2}$$

Multiply 4 and -2 to get -8.

$$-\frac{13}{36}+\frac{-8}{9}+\frac{\frac{4}{3}}{-1}-\left(\frac{5}{18}-\frac{2}{3}\right)\times \frac{3}{2}$$

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

$$-\frac{13}{36}-\frac{8}{9}+\frac{\frac{4}{3}}{-1}-\left(\frac{5}{18}-\frac{2}{3}\right)\times \frac{3}{2}$$

Least common multiple of 36 and 9 is 36. Convert -\frac{13}{36} and \frac{8}{9} to fractions with denominator 36.

$$-\frac{13}{36}-\frac{32}{36}+\frac{\frac{4}{3}}{-1}-\left(\frac{5}{18}-\frac{2}{3}\right)\times \frac{3}{2}$$

Since -\frac{13}{36} and \frac{32}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-13-32}{36}+\frac{\frac{4}{3}}{-1}-\left(\frac{5}{18}-\frac{2}{3}\right)\times \frac{3}{2}$$

Subtract 32 from -13 to get -45.

$$\frac{-45}{36}+\frac{\frac{4}{3}}{-1}-\left(\frac{5}{18}-\frac{2}{3}\right)\times \frac{3}{2}$$

Reduce the fraction \frac{-45}{36} to lowest terms by extracting and canceling out 9.

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

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

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

Multiply 3 and -1 to get -3.

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

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

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

Least common multiple of 4 and 3 is 12. Convert -\frac{5}{4} and \frac{4}{3} to fractions with denominator 12.

$$-\frac{15}{12}-\frac{16}{12}-\left(\frac{5}{18}-\frac{2}{3}\right)\times \frac{3}{2}$$

Since -\frac{15}{12} and \frac{16}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-15-16}{12}-\left(\frac{5}{18}-\frac{2}{3}\right)\times \frac{3}{2}$$

Subtract 16 from -15 to get -31.

$$-\frac{31}{12}-\left(\frac{5}{18}-\frac{2}{3}\right)\times \frac{3}{2}$$

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

$$-\frac{31}{12}-\left(\frac{5}{18}-\frac{12}{18}\right)\times \frac{3}{2}$$

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

$$-\frac{31}{12}-\frac{5-12}{18}\times \frac{3}{2}$$

Subtract 12 from 5 to get -7.

$$-\frac{31}{12}-\left(-\frac{7}{18}\times \frac{3}{2}\right)$$

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

$$-\frac{31}{12}-\frac{-7\times 3}{18\times 2}$$

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

$$-\frac{31}{12}-\frac{-21}{36}$$

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

$$-\frac{31}{12}-\left(-\frac{7}{12}\right)$$

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

$$-\frac{31}{12}+\frac{7}{12}$$

Since -\frac{31}{12} and \frac{7}{12} have the same denominator, add them by adding their numerators.

$$\frac{-31+7}{12}$$

Add -31 and 7 to get -24.

$$\frac{-24}{12}$$

Divide -24 by 12 to get -2.

$$-2$$

Factor

$$-2$$