Solve 200left(40*120-50*40right)^2/80*120*110*90

$$\frac{ 200 { \left(40 \cdot 120-50 \cdot 40 \right) }^{ 2 } }{ 80 \cdot 120 \cdot 110 \cdot 90 }$$

Evaluate

$$\frac{4900}{297}\approx 16.498316498$$

Solution Steps

Cancel out 5\times 40 in both numerator and denominator.

$$\frac{\left(40\times 120-40\times 50\right)^{2}}{2\times 24\times 90\times 110}$$

Multiply 40 and 120 to get 4800.

$$\frac{\left(4800-40\times 50\right)^{2}}{2\times 24\times 90\times 110}$$

Multiply 40 and 50 to get 2000.

$$\frac{\left(4800-2000\right)^{2}}{2\times 24\times 90\times 110}$$

Subtract 2000 from 4800 to get 2800.

$$\frac{2800^{2}}{2\times 24\times 90\times 110}$$

Calculate 2800 to the power of 2 and get 7840000.

$$\frac{7840000}{2\times 24\times 90\times 110}$$

Multiply 2 and 24 to get 48.

$$\frac{7840000}{48\times 90\times 110}$$

Multiply 48 and 90 to get 4320.

$$\frac{7840000}{4320\times 110}$$

Multiply 4320 and 110 to get 475200.

$$\frac{7840000}{475200}$$

Reduce the fraction \frac{7840000}{475200} to lowest terms by extracting and canceling out 1600.

$$\frac{4900}{297}$$

Factor

$$\frac{2 ^ {2} \cdot 5 ^ {2} \cdot 7 ^ {2}}{3 ^ {3} \cdot 11} = 16\frac{148}{297} = 16.4983164983165$$