Solve {l}{1/36*20^3+10/3*20^2}{-200/3*20+4000/9}

$$\left. \begin{array} { l } { \frac { 1 } { 36 } \times 20 ^ { 3 } + \frac { 10 } { 3 } \times 20 ^ { 2 } } \\ { - \frac { 200 } { 3 } \times 20 + \frac { 4000 } { 9 } } \end{array} \right.$$

Evaluate

$$\frac{2000}{3}\approx 666.666666667$$

Solution Steps

Calculate 20 to the power of 3 and get 8000.

$$\frac{1}{36}\times 8000+\frac{10}{3}\times 20^{2}-\frac{200}{3}\times 20+\frac{4000}{9}$$

Multiply \frac{1}{36} and 8000 to get \frac{8000}{36}.

$$\frac{8000}{36}+\frac{10}{3}\times 20^{2}-\frac{200}{3}\times 20+\frac{4000}{9}$$

Reduce the fraction \frac{8000}{36} to lowest terms by extracting and canceling out 4.

$$\frac{2000}{9}+\frac{10}{3}\times 20^{2}-\frac{200}{3}\times 20+\frac{4000}{9}$$

Calculate 20 to the power of 2 and get 400.

$$\frac{2000}{9}+\frac{10}{3}\times 400-\frac{200}{3}\times 20+\frac{4000}{9}$$

Express \frac{10}{3}\times 400 as a single fraction.

$$\frac{2000}{9}+\frac{10\times 400}{3}-\frac{200}{3}\times 20+\frac{4000}{9}$$

Multiply 10 and 400 to get 4000.

$$\frac{2000}{9}+\frac{4000}{3}-\frac{200}{3}\times 20+\frac{4000}{9}$$

Least common multiple of 9 and 3 is 9. Convert \frac{2000}{9} and \frac{4000}{3} to fractions with denominator 9.

$$\frac{2000}{9}+\frac{12000}{9}-\frac{200}{3}\times 20+\frac{4000}{9}$$

Since \frac{2000}{9} and \frac{12000}{9} have the same denominator, add them by adding their numerators.

$$\frac{2000+12000}{9}-\frac{200}{3}\times 20+\frac{4000}{9}$$

Add 2000 and 12000 to get 14000.

$$\frac{14000}{9}-\frac{200}{3}\times 20+\frac{4000}{9}$$

Express \frac{200}{3}\times 20 as a single fraction.

$$\frac{14000}{9}-\frac{200\times 20}{3}+\frac{4000}{9}$$

Multiply 200 and 20 to get 4000.

$$\frac{14000}{9}-\frac{4000}{3}+\frac{4000}{9}$$

Least common multiple of 9 and 3 is 9. Convert \frac{14000}{9} and \frac{4000}{3} to fractions with denominator 9.

$$\frac{14000}{9}-\frac{12000}{9}+\frac{4000}{9}$$

Since \frac{14000}{9} and \frac{12000}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{14000-12000}{9}+\frac{4000}{9}$$

Subtract 12000 from 14000 to get 2000.

$$\frac{2000}{9}+\frac{4000}{9}$$

Since \frac{2000}{9} and \frac{4000}{9} have the same denominator, add them by adding their numerators.

$$\frac{2000+4000}{9}$$

Add 2000 and 4000 to get 6000.

$$\frac{6000}{9}$$

Reduce the fraction \frac{6000}{9} to lowest terms by extracting and canceling out 3.

$$\frac{2000}{3}$$

Factor

$$\frac{2 ^ {4} \cdot 5 ^ {3}}{3} = 666\frac{2}{3} = 666.6666666666666$$