A number not always represent the same thing, therefore 1 not always equal 1.

Yes, you understood correct, I'm sorry by my mistake. Words that are very close in sound sometimes makes me confused. I'll try to concentrate on your example, and go over something else that is taught in mathematics, and maybe you could understand my point better. CON wrote; "I have two groups of apples (group A and B). In each group, there is half an apple. I want to figure out how many apples from group A to send to group B. In other words, I want to "divide" my group A members evenly among my group B members. My answer will be:" If you have two groups, and each has half an apple, and you send half an apple to one group, you are left with an empty group (in this case group A). How is this dividing? If you do the same thing with whole numbers, it wouldn't work to gain the result desired. Example: Both groups A and B has 1 apple. I send one apple to group B, group B has now 2 apples. When you divide, you don't start with groups, you have one unit, and you divide that unit. After you divide, you have more than one unit since you split that unit. Let's say I have a bar of chocolate, at this point I have one unit. If I brake this unit in half, now I have 2 half pieces. This can be shown as 1/ 1/2 or 1 / 2 (one divided by two). Both times in the left (represented by the number 1), it will represent the bar of chocolate I had before splitting into 2 pieces. The first equation, the number in the right, represents which way I cut it, which was in half giving me the result of 2 pieces I acquire from that 1 unit. Second equation, the number on the right represents what would happen if I divide this into two groups evenly. Each group would both get half piece. Or you could have the answer to; after dividing the chocolate in two equal parts (groups if you prefer), what size is each part? Anyway, both times, the number in the left is the only number that represent the unit, the number in the right simply tells you what you are doing with that unit. Both numbers never represent the same role. This works great if I have a whole number, but if I have fraction, I cannot do the same, unless the other function on the right is not a fraction. Note* The result 2, even know are chocolates, should be seen as parts because, if you see as chocolates it results in 1=2. I don't know, maybe that is how my opponent arrived on 1 apple from 1/2. Try to follow what I just wrote, but this time use half of a bar of chocolate, and see what happens. If you feel what I say is wrong, please tell me which equation I should have used instead, and use both types of equation to solve both problems, 1 bar of chocolate, and a 1/2 of a bar. If you feel I was right, follow my example using half of bar instead. Now as I promise, I will show what is taught in mathematics, this is not where my thinking originated, but I got to this mathematical concept after this vision of my. Most of us should know that, multiplication is a simpler way to write addition (2+2+2 is the same as 3x2).Like multiplication, division can be written by multiples, but in reverse. So 10/2 could be written, 10-2-2-2-2-2=5. Two repeats five times, which is the answer. My idea of thinking, lead me to those types of mathematical lessons, I never learn this type of lessons in school.