every number division by the same number is 1 for example
3/3=1, 2/2=1 1/1=1 because (the same number)/(the same number)always equil 1
Not true. Look at it this way. If you have 0 pieces of pie and you divide those pieces equally among 0 people (0/0), how many pieces of pie does each person get? It isn't 1. It also isn't really equal to 0 because there aren't any people to give the pie out to. That's why division by 0 is invalid. Still, 0 is a much better answer than 1. An error would be the better answer overall.
The statement that you sometimes hear in lower level math courses (elementary/middle school level) that any number divided by itself equals 1 is a generalization meant to help students remember what 3/3 or 6/6 or 123456/123456 is equal to. Later, students are told of the exception to the rule, where 0/0 is not equal to 1. There are other types of generalizations that are used when teaching math and then once you get those down, you are taught the exceptions. It's easier than starting out by telling a student that "this is true except when this is true or when that is true or when this happens."
It's similar to teaching a language, such as English. You don't jump in and tell students every possible sound a vowel like "a" or "e" makes. Instead, you give them generalizations. "If a word as 'ea' together, then the 'e' is long and the 'a' is silent." In most cases, that's true and a good start for teaching the two-vowel sounds. However, it's not always true. For example, "instead". Or you generalize that a vowel between two consonants is short. That's true much of the time, but there are exceptions (toll, make, there). However, you don't start teaching the exceptions right away or you confuse the students. Especially since the English language seems to have more exceptions than rules. It's the same with math. Many of the "rules" have exceptions that you need to be aware of.
