Solve (-729/10-1/5-36/3+12/4)*frac{pi}{2}

$$( - \frac { 729 } { 10 } - \frac { 1 } { 5 } - \frac { 36 } { 3 } + \frac { 12 } { 4 } ) \cdot \frac { \pi } { 2 }$$

Evaluate

$$-\frac{821\pi }{20}\approx -128.96237843$$

Solution Steps

Least common multiple of 10 and 5 is 10. Convert -\frac{729}{10} and \frac{1}{5} to fractions with denominator 10.

$$\left(-\frac{729}{10}-\frac{2}{10}-\frac{36}{3}+\frac{12}{4}\right)\times \frac{\pi }{2}$$

Since -\frac{729}{10} and \frac{2}{10} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{-729-2}{10}-\frac{36}{3}+\frac{12}{4}\right)\times \frac{\pi }{2}$$

Subtract 2 from -729 to get -731.

$$\left(-\frac{731}{10}-\frac{36}{3}+\frac{12}{4}\right)\times \frac{\pi }{2}$$

Divide 36 by 3 to get 12.

$$\left(-\frac{731}{10}-12+\frac{12}{4}\right)\times \frac{\pi }{2}$$

Convert 12 to fraction \frac{120}{10}.

$$\left(-\frac{731}{10}-\frac{120}{10}+\frac{12}{4}\right)\times \frac{\pi }{2}$$

Since -\frac{731}{10} and \frac{120}{10} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{-731-120}{10}+\frac{12}{4}\right)\times \frac{\pi }{2}$$

Subtract 120 from -731 to get -851.

$$\left(-\frac{851}{10}+\frac{12}{4}\right)\times \frac{\pi }{2}$$

Divide 12 by 4 to get 3.

$$\left(-\frac{851}{10}+3\right)\times \frac{\pi }{2}$$

Convert 3 to fraction \frac{30}{10}.

$$\left(-\frac{851}{10}+\frac{30}{10}\right)\times \frac{\pi }{2}$$

Since -\frac{851}{10} and \frac{30}{10} have the same denominator, add them by adding their numerators.

$$\frac{-851+30}{10}\times \frac{\pi }{2}$$

Add -851 and 30 to get -821.

$$-\frac{821}{10}\times \frac{\pi }{2}$$

Multiply -\frac{821}{10} times \frac{\pi }{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-821\pi }{10\times 2}$$

Multiply 10 and 2 to get 20.

$$\frac{-821\pi }{20}$$

Expand

$$-\frac{821 \pi}{20} = -128.962378429861$$

Solution Steps

Least common multiple of 10 and 5 is 10. Convert -\frac{729}{10} and \frac{1}{5} to fractions with denominator 10.

$$\left(-\frac{729}{10}-\frac{2}{10}-\frac{36}{3}+\frac{12}{4}\right)\times \frac{\pi }{2}$$

Since -\frac{729}{10} and \frac{2}{10} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{-729-2}{10}-\frac{36}{3}+\frac{12}{4}\right)\times \frac{\pi }{2}$$

Subtract 2 from -729 to get -731.

$$\left(-\frac{731}{10}-\frac{36}{3}+\frac{12}{4}\right)\times \frac{\pi }{2}$$

Divide 36 by 3 to get 12.

$$\left(-\frac{731}{10}-12+\frac{12}{4}\right)\times \frac{\pi }{2}$$

Convert 12 to fraction \frac{120}{10}.

$$\left(-\frac{731}{10}-\frac{120}{10}+\frac{12}{4}\right)\times \frac{\pi }{2}$$

Since -\frac{731}{10} and \frac{120}{10} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{-731-120}{10}+\frac{12}{4}\right)\times \frac{\pi }{2}$$

Subtract 120 from -731 to get -851.

$$\left(-\frac{851}{10}+\frac{12}{4}\right)\times \frac{\pi }{2}$$

Divide 12 by 4 to get 3.

$$\left(-\frac{851}{10}+3\right)\times \frac{\pi }{2}$$

Convert 3 to fraction \frac{30}{10}.

$$\left(-\frac{851}{10}+\frac{30}{10}\right)\times \frac{\pi }{2}$$

Since -\frac{851}{10} and \frac{30}{10} have the same denominator, add them by adding their numerators.

$$\frac{-851+30}{10}\times \frac{\pi }{2}$$

Add -851 and 30 to get -821.

$$-\frac{821}{10}\times \frac{\pi }{2}$$

Multiply -\frac{821}{10} times \frac{\pi }{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-821\pi }{10\times 2}$$

Multiply 10 and 2 to get 20.

$$\frac{-821\pi }{20}$$