Solve 200left(65*45-35*55right)^2/100*100*110*90

$$200 \frac{ { \left(65 \cdot 45-35 \cdot 55 \right) }^{ 2 } }{ 100 \times 100 \times 110 \times 90 }$$

Evaluate

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

Solution Steps

Multiply 65 and 45 to get 2925.

$$200\times \frac{\left(2925-35\times 55\right)^{2}}{100\times 100\times 110\times 90}$$

Multiply 35 and 55 to get 1925.

$$200\times \frac{\left(2925-1925\right)^{2}}{100\times 100\times 110\times 90}$$

Subtract 1925 from 2925 to get 1000.

$$200\times \frac{1000^{2}}{100\times 100\times 110\times 90}$$

Calculate 1000 to the power of 2 and get 1000000.

$$200\times \frac{1000000}{100\times 100\times 110\times 90}$$

Multiply 100 and 100 to get 10000.

$$200\times \frac{1000000}{10000\times 110\times 90}$$

Multiply 10000 and 110 to get 1100000.

$$200\times \frac{1000000}{1100000\times 90}$$

Multiply 1100000 and 90 to get 99000000.

$$200\times \frac{1000000}{99000000}$$

Reduce the fraction \frac{1000000}{99000000} to lowest terms by extracting and canceling out 1000000.

$$200\times \frac{1}{99}$$

Multiply 200 and \frac{1}{99} to get \frac{200}{99}.

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

Factor

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