Tony's Responses in WyzAnt Answers

The lowest common multiple of 1/2 and of 1/4 is 4.

That is 2 * 2 = 4 and 1*4 = 4.

So multiply through by the lowest common multiple (LCM).

4*(7/2) + 4*x = 4*(1/4)
28/2 + 4x = 4/4
14 + 4x = 1
4x = -13
x=-13/4

To answer this, first let's consider some other cases. 

6 divided by 6 = 1. 

6 divided by 3 = 2.

6 divided by 2 = 3.

6 divided by 1 = 6.

Let us pretend these are apples.  So in the first case, I am asking to divide 6 apples into 6 groups.  How many apples are in each group?  Well, only 1.  If I put 1 apple into 6 different spots on my kitchen table, I will have 6 groups of apples.

I then take the 6 apples and divide them into 3 groups.  When I divide them out over the kitchen table, I then find I have 2 apples in each group.  So I have 3 groups of 2 apples.

For the third option and fourth option above, I am separating the apples into 2 groups of 3 and then just 1 group.  So all 6 apples end up in just 1 group.

We then ask ourselves what is 6 divided by 0.  I want to take my six apples and divide them into zero groups.  Well... I can't just make the apples disappear.  I am still stuck with 6 apples.  But if even if I have all six apples in one spot on the table, there would still be 1 group of apples, not 0 groups of apples. 

There is no way to evenly divide something up into 0 parts.  You could say, I'll form parts that are smaller than "1"... say... 0.5 ... or 0.25 or 0.125 ... getting smaller and smaller like on a ruler when you are dividing up 1 inch into pieces.  However, you will always be dividing it up into SOMETHING..