Well, you have something of the form:
The m's don't cancel out because m AND k are divided by m. But you could rearrange this to:
Hi, please can someone watch this video here?
YouTube - Rearranging.flv
I can follow it right up to the part just before she takes the square root of both sides of the equation. What I don't get is the whole of the video before this point goes on about what you do to the left of the equation you have to do to the other side of the equation too. But in this section she has and but she only removes the m from the left hand side. Surely she should get rid of m from both sides to be consistent before going on to take the square roots of both sides of the equation?
YouTube - Rearranging.flv
Basically the question is why do the two m's on the right side of the equation not cancel out? It's rather amusing how they laugh heartily but make no effort to explain this.
So are you just saying thatWell, you have something of the form:
But you could rearrange this to:
and are exactly equivalent?
I'm slightly lost here. I would have assumed that would require that you do the 'opposite' from what's in the equation? So since you have you would have to somehow subtract from the top and from the bottom and then divide them? Can you please break your logic down into smaller steps and explain them in English where possible too?
then we can add them by getting a common denominator. The common denominator in this case will be 4 x 5 = 20. So we need to multiply the fraction on the right to put it in the form (something)/20.
Now, we can't change the value of 1/5, but we must find a way to multiply the denominator by a factor of 4. How can we do this? Well if we multiply the fraction 1/5 by 1, then we still have 1/5. So I'm going to choose a particular kind of form of 1 to multiply the 1/5 by.
We do the same thing with 3/4, but in this case we need to multiply the denominator by 5, thus
Why do we do all this? In order to add two fractions we need to have a common denominator, in this case 20.
The problem you are being asked to do is very similar, except in this case I'm going to change the 1 into 1/1, so we can have the number 1 in fractional form. So how do you add
The eventual point of all this is to show that . Do you see the similarities?
But I think I've lost the thread a little on how this relates to the original question? In the case of everything on either side of the plus sign is being divided by m, so the m's don't cancel? But in the case of which is closer to my original example, they do seem to cancel?The eventual point of all this is to show that . Do you see the similarities?
YouTube - Rearranging.flv the reason (or rule) why both m's don't cancel is because one side of the equation contains factors and the other contains terms? So only calculations like this with factors as the numerator (above the denominator) would tend to cancel, while those (as on the right side of the equation here) that use terms as the numerator would not?