Solve 110*(50*20-30*10)^2/60*50*30*80

$$\frac { 110 \times ( 50 \times 20 - 30 \times 10 ) ^ { 2 } } { 60 \times 50 \times 30 \times 80 }$$

Evaluate

$$\frac{539}{72}\approx 7.486111111$$

Solution Steps

Cancel out 10 in both numerator and denominator.

$$\frac{11\left(20\times 50-10\times 30\right)^{2}}{6\times 30\times 50\times 80}$$

Multiply 20 and 50 to get 1000.

$$\frac{11\left(1000-10\times 30\right)^{2}}{6\times 30\times 50\times 80}$$

Multiply 10 and 30 to get 300.

$$\frac{11\left(1000-300\right)^{2}}{6\times 30\times 50\times 80}$$

Subtract 300 from 1000 to get 700.

$$\frac{11\times 700^{2}}{6\times 30\times 50\times 80}$$

Calculate 700 to the power of 2 and get 490000.

$$\frac{11\times 490000}{6\times 30\times 50\times 80}$$

Multiply 11 and 490000 to get 5390000.

$$\frac{5390000}{6\times 30\times 50\times 80}$$

Multiply 6 and 30 to get 180.

$$\frac{5390000}{180\times 50\times 80}$$

Multiply 180 and 50 to get 9000.

$$\frac{5390000}{9000\times 80}$$

Multiply 9000 and 80 to get 720000.

$$\frac{5390000}{720000}$$

Reduce the fraction \frac{5390000}{720000} to lowest terms by extracting and canceling out 10000.

$$\frac{539}{72}$$

Factor

$$\frac{7 ^ {2} \cdot 11}{2 ^ {3} \cdot 3 ^ {2}} = 7\frac{35}{72} = 7.486111111111111$$