Solve -27/20*(-5/9)-5/24*(-22/5)

$$- \frac { 27 } { 20 } \cdot ( - \frac { 5 } { 9 } ) - \frac { 5 } { 24 } \cdot ( - \frac { 22 } { 5 } )$$

Evaluate

$$\frac{5}{3}\approx 1.666666667$$

Solution Steps

Multiply -\frac{27}{20} times -\frac{5}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-27\left(-5\right)}{20\times 9}-\frac{5}{24}\left(-\frac{22}{5}\right)$$

Do the multiplications in the fraction \frac{-27\left(-5\right)}{20\times 9}.

$$\frac{135}{180}-\frac{5}{24}\left(-\frac{22}{5}\right)$$

Reduce the fraction \frac{135}{180} to lowest terms by extracting and canceling out 45.

$$\frac{3}{4}-\frac{5}{24}\left(-\frac{22}{5}\right)$$

Multiply \frac{5}{24} times -\frac{22}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3}{4}-\frac{5\left(-22\right)}{24\times 5}$$

Cancel out 5 in both numerator and denominator.

$$\frac{3}{4}-\frac{-22}{24}$$

Reduce the fraction \frac{-22}{24} to lowest terms by extracting and canceling out 2.

$$\frac{3}{4}-\left(-\frac{11}{12}\right)$$

The opposite of -\frac{11}{12} is \frac{11}{12}.

$$\frac{3}{4}+\frac{11}{12}$$

Least common multiple of 4 and 12 is 12. Convert \frac{3}{4} and \frac{11}{12} to fractions with denominator 12.

$$\frac{9}{12}+\frac{11}{12}$$

Since \frac{9}{12} and \frac{11}{12} have the same denominator, add them by adding their numerators.

$$\frac{9+11}{12}$$

Add 9 and 11 to get 20.

$$\frac{20}{12}$$

Reduce the fraction \frac{20}{12} to lowest terms by extracting and canceling out 4.

$$\frac{5}{3}$$

Factor

$$\frac{5}{3} = 1\frac{2}{3} = 1.6666666666666667$$