Solve 3272/990*(-11/6)+48/13*3/105+frac{5}{9}

$$\frac { 3272 } { 990 } \cdot ( - \frac { 11 } { 6 } ) + \frac { 48 } { 13 } \cdot \frac { 3 } { 105 } + \frac { 5 } { 9 }$$

Evaluate

$$-\frac{66317}{12285}\approx -5.398209198$$

Solution Steps

Reduce the fraction \frac{3272}{990} to lowest terms by extracting and canceling out 2.

$$\frac{1636}{495}\left(-\frac{11}{6}\right)+\frac{48}{13}\times \frac{3}{105}+\frac{5}{9}$$

Multiply \frac{1636}{495} times -\frac{11}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1636\left(-11\right)}{495\times 6}+\frac{48}{13}\times \frac{3}{105}+\frac{5}{9}$$

Do the multiplications in the fraction \frac{1636\left(-11\right)}{495\times 6}.

$$\frac{-17996}{2970}+\frac{48}{13}\times \frac{3}{105}+\frac{5}{9}$$

Reduce the fraction \frac{-17996}{2970} to lowest terms by extracting and canceling out 22.

$$-\frac{818}{135}+\frac{48}{13}\times \frac{3}{105}+\frac{5}{9}$$

Reduce the fraction \frac{3}{105} to lowest terms by extracting and canceling out 3.

$$-\frac{818}{135}+\frac{48}{13}\times \frac{1}{35}+\frac{5}{9}$$

Multiply \frac{48}{13} times \frac{1}{35} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{818}{135}+\frac{48\times 1}{13\times 35}+\frac{5}{9}$$

Do the multiplications in the fraction \frac{48\times 1}{13\times 35}.

$$-\frac{818}{135}+\frac{48}{455}+\frac{5}{9}$$

Least common multiple of 135 and 455 is 12285. Convert -\frac{818}{135} and \frac{48}{455} to fractions with denominator 12285.

$$-\frac{74438}{12285}+\frac{1296}{12285}+\frac{5}{9}$$

Since -\frac{74438}{12285} and \frac{1296}{12285} have the same denominator, add them by adding their numerators.

$$\frac{-74438+1296}{12285}+\frac{5}{9}$$

Add -74438 and 1296 to get -73142.

$$-\frac{73142}{12285}+\frac{5}{9}$$

Least common multiple of 12285 and 9 is 12285. Convert -\frac{73142}{12285} and \frac{5}{9} to fractions with denominator 12285.

$$-\frac{73142}{12285}+\frac{6825}{12285}$$

Since -\frac{73142}{12285} and \frac{6825}{12285} have the same denominator, add them by adding their numerators.

$$\frac{-73142+6825}{12285}$$

Add -73142 and 6825 to get -66317.

$$-\frac{66317}{12285}$$

Factor

$$-\frac{66317}{12285} = -5\frac{4892}{12285} = -5.398209198209198$$