For some reason, people who are starting to learn algebra suddenly forget all they ever knew about numbers. If you had six pieces of candy and five friends and decided to share your candy equally with your friends, the arithmetic problem that you must solve is [MATH]6 \div 6 = \text {WHAT?}[/MATH].
If that division results in zero, that means that your decision to share made all the candy disappear so that no one, including you, gets any candy at all. Best to decide not to share, but whether you decide to share or not, your friends never get any candy from you. And pretty soon, you will have zero friends.
Of course, if [MATH]6 \div 6 = 1[/MATH] rather than 0, you and your friends will all get one piece of candy.
So is the answer 0 or 1? Would the answer change if you divided 4 by 4? Every number ((except zero) divided by itself equals 1.
The letters in algebra just stand for numbers that you don't know yet. They behave according to all the laws of numbers that you learned in arithmetic.
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