Solve 100(40*15-10*35)^2/(40+10)(35+15)(40+35)(10+15)

$$\frac { 100 ( 40 \times 15 - 10 \times 35 ) ^ { 2 } } { ( 40 + 10 ) ( 35 + 15 ) ( 40 + 35 ) ( 10 + 15 ) }$$

Evaluate

$$\frac{4}{3}\approx 1.333333333$$

Solution Steps

Multiply 40 and 15 to get 600.

$$\frac{100\left(600-10\times 35\right)^{2}}{\left(40+10\right)\left(35+15\right)\left(40+35\right)\left(10+15\right)}$$

Multiply 10 and 35 to get 350.

$$\frac{100\left(600-350\right)^{2}}{\left(40+10\right)\left(35+15\right)\left(40+35\right)\left(10+15\right)}$$

Subtract 350 from 600 to get 250.

$$\frac{100\times 250^{2}}{\left(40+10\right)\left(35+15\right)\left(40+35\right)\left(10+15\right)}$$

Calculate 250 to the power of 2 and get 62500.

$$\frac{100\times 62500}{\left(40+10\right)\left(35+15\right)\left(40+35\right)\left(10+15\right)}$$

Multiply 100 and 62500 to get 6250000.

$$\frac{6250000}{\left(40+10\right)\left(35+15\right)\left(40+35\right)\left(10+15\right)}$$

Add 40 and 10 to get 50.

$$\frac{6250000}{50\left(35+15\right)\left(40+35\right)\left(10+15\right)}$$

Add 35 and 15 to get 50.

$$\frac{6250000}{50\times 50\left(40+35\right)\left(10+15\right)}$$

Multiply 50 and 50 to get 2500.

$$\frac{6250000}{2500\left(40+35\right)\left(10+15\right)}$$

Add 40 and 35 to get 75.

$$\frac{6250000}{2500\times 75\left(10+15\right)}$$

Multiply 2500 and 75 to get 187500.

$$\frac{6250000}{187500\left(10+15\right)}$$

Add 10 and 15 to get 25.

$$\frac{6250000}{187500\times 25}$$

Multiply 187500 and 25 to get 4687500.

$$\frac{6250000}{4687500}$$

Reduce the fraction \frac{6250000}{4687500} to lowest terms by extracting and canceling out 1562500.

$$\frac{4}{3}$$

Factor

$$\frac{2 ^ {2}}{3} = 1\frac{1}{3} = 1.3333333333333333$$