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

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

Evaluate

$$\frac{\pi +33}{36}\approx 1.003933129$$

Short Solution Steps

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

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

Cancel out 5 in both numerator and denominator.

$$\frac{\pi }{4\times 9}-\frac{5}{24}\left(-\frac{22}{5}\right)$$

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

$$\frac{\pi }{4\times 9}-\frac{5\left(-22\right)}{24\times 5}$$

Cancel out 5 in both numerator and denominator.

$$\frac{\pi }{4\times 9}-\frac{-22}{24}$$

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

$$\frac{\pi }{4\times 9}-\left(-\frac{11}{12}\right)$$

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

$$\frac{\pi }{4\times 9}+\frac{11}{12}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4\times 9 and 12 is 36. Multiply \frac{11}{12} times \frac{3}{3}.

$$\frac{\pi }{36}+\frac{11\times 3}{36}$$

Since \frac{\pi }{36} and \frac{11\times 3}{36} have the same denominator, add them by adding their numerators.

$$\frac{\pi +11\times 3}{36}$$

Do the multiplications in \pi +11\times 3.

$$\frac{\pi +33}{36}$$

Factor

$$\frac{\pi + 33}{36} = 1.0039331292663833$$