Solve 200*(60*20+30*90)^2/150*50*90*110

$$\frac { 200 \times ( 60 \times 20 + 30 \times 90 ) ^ { 2 } } { 150 \times 50 \times 90 \times 110 }$$

Evaluate

$$\frac{1352}{33}\approx 40.96969697$$

Solution Steps

Cancel out 2\times 2\times 50 in both numerator and denominator.

$$\frac{\left(20\times 60+30\times 90\right)^{2}}{3\times 25\times 45\times 110}$$

Do the multiplications.

$$\frac{\left(1200+2700\right)^{2}}{3\times 25\times 45\times 110}$$

Add 1200 and 2700 to get 3900.

$$\frac{3900^{2}}{3\times 25\times 45\times 110}$$

Calculate 3900 to the power of 2 and get 15210000.

$$\frac{15210000}{3\times 25\times 45\times 110}$$

Multiply 3 and 25 to get 75.

$$\frac{15210000}{75\times 45\times 110}$$

Multiply 75 and 45 to get 3375.

$$\frac{15210000}{3375\times 110}$$

Multiply 3375 and 110 to get 371250.

$$\frac{15210000}{371250}$$

Reduce the fraction \frac{15210000}{371250} to lowest terms by extracting and canceling out 11250.

$$\frac{1352}{33}$$

Factor

$$\frac{2 ^ {3} \cdot 13 ^ {2}}{3 \cdot 11} = 40\frac{32}{33} = 40.96969696969697$$