In this explanation of the answer, it tells us to "divide the product by and you get 6. why do you have to divide by ?

is referring to getting the LCD, least common divisor, namely a value/expression that is divisible by all three factors, but is the least or smallest possible off many.

it doesn't give a good reason why divide by x exactly, but lemme give you another way to get the LCD.

we have three denominators from whom we'd want the LCD, 3, x, and 2x.

3 and x have no factors in common, so we use their product, 3*x or 3x.

now 3x and 2x have x in as a common factor, so we only include it in the LCD once, so the factors for the LCD will end up as 3*x*2 <--- x used only once, because of being common in two of the denominators.

3*x*2 = 6x.

say for example we have three numbers, say they're denominators for example's sake, 15, 6 and 30.

first off we break them out in factors, usually called "prime factoring".

15 = 3 * 5

6 = 2 * 3

30 = 2 * 3 * 5

from (3*5) and (2*3), we see the 3 is repeated, or in both, so we use it once, so the LCD of those two is only 3*5*2, using the 3 only once.

now we need to get the LCD of the one we just found and the remaining 2*3*5.

well, the LCD of the other two is (3*5*2) and the remaining denominator is (2*3*5), but notice, 3 is in both, 2 is in both and 5 is in both, holly guacamole!! since 3, 2 and 5 are repeated, we use them only once, 3*5*2, thus that is the LCD 3*5*2 namely 30.

Miles per gallon stands for the amount of miles traveled divided by how many gallons of gasoline were used to get there.

We'll want to divide each (miles/gallons) to figure out the answer.

Try using a calculator to figure it out, I know you can do it! If you're still having trouble, let me know and I'll walk you through each and every step.