Solve =2/3*22/7*3/2*frac{3/2*frac{3}{2}*1000}{frac{25}{7}}

$$= \frac { \frac { 2 } { 3 } \times \frac { 22 } { 7 } \times \frac { 3 } { 2 } \times \frac { 3 } { 2 } \times \frac { 3 } { 2 } \times 1000 } { \frac { 25 } { 7 } }$$

Evaluate

$$1980$$

Solution Steps

Multiply \frac{2}{3} times \frac{22}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{2\times 22}{3\times 7}\times \frac{3}{2}\times \frac{3}{2}\times \frac{3}{2}\times 1000}{\frac{25}{7}}$$

Do the multiplications in the fraction \frac{2\times 22}{3\times 7}.

$$\frac{\frac{44}{21}\times \frac{3}{2}\times \frac{3}{2}\times \frac{3}{2}\times 1000}{\frac{25}{7}}$$

Multiply \frac{44}{21} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{44\times 3}{21\times 2}\times \frac{3}{2}\times \frac{3}{2}\times 1000}{\frac{25}{7}}$$

Do the multiplications in the fraction \frac{44\times 3}{21\times 2}.

$$\frac{\frac{132}{42}\times \frac{3}{2}\times \frac{3}{2}\times 1000}{\frac{25}{7}}$$

Reduce the fraction \frac{132}{42} to lowest terms by extracting and canceling out 6.

$$\frac{\frac{22}{7}\times \frac{3}{2}\times \frac{3}{2}\times 1000}{\frac{25}{7}}$$

Multiply \frac{22}{7} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{22\times 3}{7\times 2}\times \frac{3}{2}\times 1000}{\frac{25}{7}}$$

Do the multiplications in the fraction \frac{22\times 3}{7\times 2}.

$$\frac{\frac{66}{14}\times \frac{3}{2}\times 1000}{\frac{25}{7}}$$

Reduce the fraction \frac{66}{14} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{33}{7}\times \frac{3}{2}\times 1000}{\frac{25}{7}}$$

Multiply \frac{33}{7} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{33\times 3}{7\times 2}\times 1000}{\frac{25}{7}}$$

Do the multiplications in the fraction \frac{33\times 3}{7\times 2}.

$$\frac{\frac{99}{14}\times 1000}{\frac{25}{7}}$$

Express \frac{99}{14}\times 1000 as a single fraction.

$$\frac{\frac{99\times 1000}{14}}{\frac{25}{7}}$$

Multiply 99 and 1000 to get 99000.

$$\frac{\frac{99000}{14}}{\frac{25}{7}}$$

Reduce the fraction \frac{99000}{14} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{49500}{7}}{\frac{25}{7}}$$

Divide \frac{49500}{7} by \frac{25}{7} by multiplying \frac{49500}{7} by the reciprocal of \frac{25}{7}.

$$\frac{49500}{7}\times \frac{7}{25}$$

Multiply \frac{49500}{7} times \frac{7}{25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{49500\times 7}{7\times 25}$$

Cancel out 7 in both numerator and denominator.

$$\frac{49500}{25}$$

Divide 49500 by 25 to get 1980.

$$1980$$

Factor

$$2^{2}\times 3^{2}\times 5\times 11$$