Solve 200left(50*40-50*60right)^2/110*90*100*100

$$\frac{ 200 { \left(50 \cdot 40-50 \cdot 60 \right) }^{ 2 } }{ 110 \cdot 90 \cdot 100 \cdot 100 }$$

Evaluate

$$\frac{200}{99}\approx 2.02020202$$

Solution Steps

Cancel out 2\times 10\times 10 in both numerator and denominator.

$$\frac{\left(40\times 50-50\times 60\right)^{2}}{9\times 11\times 50\times 100}$$

Multiply 40 and 50 to get 2000.

$$\frac{\left(2000-50\times 60\right)^{2}}{9\times 11\times 50\times 100}$$

Multiply 50 and 60 to get 3000.

$$\frac{\left(2000-3000\right)^{2}}{9\times 11\times 50\times 100}$$

Subtract 3000 from 2000 to get -1000.

$$\frac{\left(-1000\right)^{2}}{9\times 11\times 50\times 100}$$

Calculate -1000 to the power of 2 and get 1000000.

$$\frac{1000000}{9\times 11\times 50\times 100}$$

Multiply 9 and 11 to get 99.

$$\frac{1000000}{99\times 50\times 100}$$

Multiply 99 and 50 to get 4950.

$$\frac{1000000}{4950\times 100}$$

Multiply 4950 and 100 to get 495000.

$$\frac{1000000}{495000}$$

Reduce the fraction \frac{1000000}{495000} to lowest terms by extracting and canceling out 5000.

$$\frac{200}{99}$$

Factor

$$\frac{2 ^ {3} \cdot 5 ^ {2}}{3 ^ {2} \cdot 11} = 2\frac{2}{99} = 2.0202020202020203$$