Solve =1-6(72+1/2+2+1/2)/990

$$= 1 - \frac { 6 ( 72 + \frac { 1 } { 2 } + 2 + \frac { 1 } { 2 } ) } { 990 }$$

Evaluate

$$\frac{6}{11}\approx 0.545454545$$

Solution Steps

Convert 72 to fraction \frac{144}{2}.

$$1-\frac{6\left(\frac{144}{2}+\frac{1}{2}+2+\frac{1}{2}\right)}{990}$$

Since \frac{144}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$1-\frac{6\left(\frac{144+1}{2}+2+\frac{1}{2}\right)}{990}$$

Add 144 and 1 to get 145.

$$1-\frac{6\left(\frac{145}{2}+2+\frac{1}{2}\right)}{990}$$

Convert 2 to fraction \frac{4}{2}.

$$1-\frac{6\left(\frac{145}{2}+\frac{4}{2}+\frac{1}{2}\right)}{990}$$

Since \frac{145}{2} and \frac{4}{2} have the same denominator, add them by adding their numerators.

$$1-\frac{6\left(\frac{145+4}{2}+\frac{1}{2}\right)}{990}$$

Add 145 and 4 to get 149.

$$1-\frac{6\left(\frac{149}{2}+\frac{1}{2}\right)}{990}$$

Since \frac{149}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$1-\frac{6\times \frac{149+1}{2}}{990}$$

Add 149 and 1 to get 150.

$$1-\frac{6\times \frac{150}{2}}{990}$$

Divide 150 by 2 to get 75.

$$1-\frac{6\times 75}{990}$$

Multiply 6 and 75 to get 450.

$$1-\frac{450}{990}$$

Reduce the fraction \frac{450}{990} to lowest terms by extracting and canceling out 90.

$$1-\frac{5}{11}$$

Convert 1 to fraction \frac{11}{11}.

$$\frac{11}{11}-\frac{5}{11}$$

Since \frac{11}{11} and \frac{5}{11} have the same denominator, subtract them by subtracting their numerators.

$$\frac{11-5}{11}$$

Subtract 5 from 11 to get 6.

$$\frac{6}{11}$$

Factor

$$\frac{2 \cdot 3}{11} = 0.5454545454545454$$