Why it works
02282012, 08:04 AM


This works when you think of it algebraically. Let's start with an example where we have an unknown. 4/n = 1/2. In order to solve, I would want to isolate n, but I would want it to be a numerator and not a denominator. This would mean that I would multiply both sides by n, which gives me 4 = 1n/2. Now to undo the division by 2 and isolate n, I would multiply by 2, which gives me 8=n. I can do these same steps without an unknown because I am doing the same thing to both sides of the equation which balances it out. Often when cross multiplication is taught, the algebra is left out and so we can become confused as to why it works. When comparing 2 numbers, we don't know if they are =, >, or <, but I can find that out after I get rid of the denominators. Here is an example:
1/2 and 3/4
I could make this look like a numerical equation but leave out the equal sign
1/2 ___ 3/4 (the ____ represents either =, >, or <
Multiplying both sides by 2, I get
1 ____ 6/4
Then multiply both sides by 4, and I get
4 ____ 6
Well 4<6 so 1/2 < 3/4
Hope this helps. I just taught this concept yesterday and didn't go into the algebra stuff, so I might do that today!
