Solve 1/9div4/11-133/2+4/9(-2)+frac{4}{3}(-1)-(frac{3}{13}-frac{2}{3})

$$\frac { 1 } { 9 } \div \frac { 4 } { 11 } - 1 \frac { 33 } { 2 } + \frac { 4 } { 9 } ( - 2 ) + \frac { 4 } { 3 } ( - 1 ) - ( \frac { 3 } { 13 } - \frac { 2 } { 3 } )$$

Evaluate

$$-\frac{987}{52}\approx -18.980769231$$

Solution Steps

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

$$\frac{1}{9}\times \frac{11}{4}-\frac{1\times 2+33}{2}+\frac{4}{9}\left(-2\right)+\frac{4}{3}\left(-1\right)-\left(\frac{3}{13}-\frac{2}{3}\right)$$

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

$$\frac{1\times 11}{9\times 4}-\frac{1\times 2+33}{2}+\frac{4}{9}\left(-2\right)+\frac{4}{3}\left(-1\right)-\left(\frac{3}{13}-\frac{2}{3}\right)$$

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

$$\frac{11}{36}-\frac{1\times 2+33}{2}+\frac{4}{9}\left(-2\right)+\frac{4}{3}\left(-1\right)-\left(\frac{3}{13}-\frac{2}{3}\right)$$

Multiply 1 and 2 to get 2.

$$\frac{11}{36}-\frac{2+33}{2}+\frac{4}{9}\left(-2\right)+\frac{4}{3}\left(-1\right)-\left(\frac{3}{13}-\frac{2}{3}\right)$$

Add 2 and 33 to get 35.

$$\frac{11}{36}-\frac{35}{2}+\frac{4}{9}\left(-2\right)+\frac{4}{3}\left(-1\right)-\left(\frac{3}{13}-\frac{2}{3}\right)$$

Least common multiple of 36 and 2 is 36. Convert \frac{11}{36} and \frac{35}{2} to fractions with denominator 36.

$$\frac{11}{36}-\frac{630}{36}+\frac{4}{9}\left(-2\right)+\frac{4}{3}\left(-1\right)-\left(\frac{3}{13}-\frac{2}{3}\right)$$

Since \frac{11}{36} and \frac{630}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{11-630}{36}+\frac{4}{9}\left(-2\right)+\frac{4}{3}\left(-1\right)-\left(\frac{3}{13}-\frac{2}{3}\right)$$

Subtract 630 from 11 to get -619.

$$-\frac{619}{36}+\frac{4}{9}\left(-2\right)+\frac{4}{3}\left(-1\right)-\left(\frac{3}{13}-\frac{2}{3}\right)$$

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

$$-\frac{619}{36}+\frac{4\left(-2\right)}{9}+\frac{4}{3}\left(-1\right)-\left(\frac{3}{13}-\frac{2}{3}\right)$$

Multiply 4 and -2 to get -8.

$$-\frac{619}{36}+\frac{-8}{9}+\frac{4}{3}\left(-1\right)-\left(\frac{3}{13}-\frac{2}{3}\right)$$

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

$$-\frac{619}{36}-\frac{8}{9}+\frac{4}{3}\left(-1\right)-\left(\frac{3}{13}-\frac{2}{3}\right)$$

Least common multiple of 36 and 9 is 36. Convert -\frac{619}{36} and \frac{8}{9} to fractions with denominator 36.

$$-\frac{619}{36}-\frac{32}{36}+\frac{4}{3}\left(-1\right)-\left(\frac{3}{13}-\frac{2}{3}\right)$$

Since -\frac{619}{36} and \frac{32}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-619-32}{36}+\frac{4}{3}\left(-1\right)-\left(\frac{3}{13}-\frac{2}{3}\right)$$

Subtract 32 from -619 to get -651.

$$\frac{-651}{36}+\frac{4}{3}\left(-1\right)-\left(\frac{3}{13}-\frac{2}{3}\right)$$

Reduce the fraction \frac{-651}{36} to lowest terms by extracting and canceling out 3.

$$-\frac{217}{12}+\frac{4}{3}\left(-1\right)-\left(\frac{3}{13}-\frac{2}{3}\right)$$

Multiply \frac{4}{3} and -1 to get -\frac{4}{3}.

$$-\frac{217}{12}-\frac{4}{3}-\left(\frac{3}{13}-\frac{2}{3}\right)$$

Least common multiple of 12 and 3 is 12. Convert -\frac{217}{12} and \frac{4}{3} to fractions with denominator 12.

$$-\frac{217}{12}-\frac{16}{12}-\left(\frac{3}{13}-\frac{2}{3}\right)$$

Since -\frac{217}{12} and \frac{16}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-217-16}{12}-\left(\frac{3}{13}-\frac{2}{3}\right)$$

Subtract 16 from -217 to get -233.

$$-\frac{233}{12}-\left(\frac{3}{13}-\frac{2}{3}\right)$$

Least common multiple of 13 and 3 is 39. Convert \frac{3}{13} and \frac{2}{3} to fractions with denominator 39.

$$-\frac{233}{12}-\left(\frac{9}{39}-\frac{26}{39}\right)$$

Since \frac{9}{39} and \frac{26}{39} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{233}{12}-\frac{9-26}{39}$$

Subtract 26 from 9 to get -17.

$$-\frac{233}{12}-\left(-\frac{17}{39}\right)$$

The opposite of -\frac{17}{39} is \frac{17}{39}.

$$-\frac{233}{12}+\frac{17}{39}$$

Least common multiple of 12 and 39 is 156. Convert -\frac{233}{12} and \frac{17}{39} to fractions with denominator 156.

$$-\frac{3029}{156}+\frac{68}{156}$$

Since -\frac{3029}{156} and \frac{68}{156} have the same denominator, add them by adding their numerators.

$$\frac{-3029+68}{156}$$

Add -3029 and 68 to get -2961.

$$\frac{-2961}{156}$$

Reduce the fraction \frac{-2961}{156} to lowest terms by extracting and canceling out 3.

$$-\frac{987}{52}$$

Factor

$$-\frac{987}{52} = -18\frac{51}{52} = -18.98076923076923$$