I didn't understand BobPursley expl

Am I doing this right?
Q. 6 toy cars are in 16in

16 divided by 6=2.66 cars p/in

How many in 64in = 64x2.66=24 cars
40in = 40x 2.66= 15 cars
104" = 104 x 2.66= 39cars

Explanation
64inches* 6cars/16inches = notice how the units inches divide out, and leaves the unit cars....

Do you mean to set up like algebra?

64in=6cars div by 16 in
I'm confused..I know in alg u do the opposite on the oth side but all I hv ever done is sub on 1 sd then add on the other or vise versa. I don't know if I multiply and what do I multiply. I think I prob making it more confus than it is..thank you for all the help

No, Bob didn't set it up that way. He simply used dimensional analysis to work the problem AND he noted to you to see that the units you don't want cancel and leaves the units you want; i.e., cars.

64 inches x (6 cars/16 inches) = 24 cars.

If you prefer, it can also be done as a proportion.
(6 cars/16 inches) = (x cars/64 inches)
Now cross multiply to get
16x=6*64
x = 6*64/16 = 24 cars

Can I throw in a note of clarification? Melissa'a answers are actually correct: what's INcorrect is the algebra that apparently gave rise to them. As Bob pointed out, the "16 divided by 6" is actually a measure of inches per car, not cars per inch. Also, the three next statements give the right answers (24, 15 and 39 cars respectively), but 64 x 2.66 is not 24, 40 x 2.66 is not 15, and 104 x 2.66 is not 39, so if you were being marked on your working, you'd have lost marks there. These equations OUGHT to read 64 / 2.66 = 24, 40 / 2.66 = 15 and 104 / 2.66 = 39.

Bob's point is that you can verify that you haven't made a silly mistake like dividing by a factor when you should have been multiplying by it by checking the dimensional consistency of the equation - and that's a good habit to get into, as mistakes like this are very easy to make. For example, if you wrote the first equation in full, you would get

64 in x 2.66 in/car = <whatever it is> in²/car

and you would be able to see immediately that that was wrong, since what you OUGHT to get is a number of cars (as opposed to a number of square inches per car, whatever that means). If you had divided the 2.66 factor into the 64 inches instead, you would have got it right, because you would get

64 in / (2.66 in/car) = <whatever it is> cars.

I'm here to help you understand the explanation provided by BobPursley. It seems that you are trying to determine the number of cars in different lengths of space. Let's break it down step by step.

First, you calculated that there are 2.66 cars in 16 inches. This calculation is correct - you divided the length (16 inches) by the number of cars (6) to find how many cars fit in one inch.

To find the number of cars in a different length, you multiplied the length by the number of cars per inch. For example, if you have 64 inches, you multiply 64 by 2.66 to get 170.24. However, since you're dealing with cars, you can't have a fraction of a car. So, you would round down and say there are 170 cars in 64 inches.

The same process applies to the other lengths. For 40 inches, you would multiply 40 by 2.66 to get 106.4. Rounding down, you would have 106 cars. And for 104 inches, you would multiply 104 by 2.66 to get 276.64. Again, rounding down, you would have 276 cars.

Regarding your question about setting it up like algebra, here's an alternative approach:

Let's say "C" represents the number of cars and "I" represents the length in inches. You want to find the value of C given a specific value of I.

We know that in 16 inches, there are 6 cars. So we can set up the equation: 16 inches = 6 cars.

Now, let's say you have a length of I inches. To find the number of cars in that length, we rearrange the equation: C cars = (I inches * 6 cars) / 16 inches.

Here, by multiplying the length (I) by the ratio of cars to inches (6/16), the unit inches cancels out, leaving us with cars - the unit we are looking for.

So, with this setup, you can calculate the number of cars in any length by plugging in the value of I. For example, if I = 64 inches, you would have (64 * 6) / 16 = 24 cars.

I hope this helps clarify the explanation and offers an alternative approach to solve the problem. If you have any further questions, feel free to ask.