Solve 100*10+300*10.5+100*11/10+10.5+11

$$\frac { 100 \times 10 + 300 \times 10.5 + 100 \times 11 } { 10 + 10.5 + 11 }$$

Evaluate

$$\frac{500}{3}\approx 166.666666667$$

Solution Steps

Multiply 100 and 10 to get 1000. Multiply 100 and 11 to get 1100.

$$\frac{1000+300\times 10.5+1100}{10+10.5+11}$$

Multiply 300 and 10.5 to get 3150.

$$\frac{1000+3150+1100}{10+10.5+11}$$

Add 1000 and 3150 to get 4150.

$$\frac{4150+1100}{10+10.5+11}$$

Add 4150 and 1100 to get 5250.

$$\frac{5250}{10+10.5+11}$$

Add 10 and 10.5 to get 20.5.

$$\frac{5250}{20.5+11}$$

Add 20.5 and 11 to get 31.5.

$$\frac{5250}{31.5}$$

Expand \frac{5250}{31.5} by multiplying both numerator and the denominator by 10.

$$\frac{52500}{315}$$

Reduce the fraction \frac{52500}{315} to lowest terms by extracting and canceling out 105.

$$\frac{500}{3}$$

Factor

$$\frac{2 ^ {2} \cdot 5 ^ {3}}{3} = 166\frac{2}{3} = 166.66666666666666$$