Many people have spent a significant amount of time on a proof for this, but here's the most straghtforward proof I can think of:
When you devide any number, you are dividing the number into units that are as big as you specify. For example, 10 / 2 divides ten into groups of 2. You'll end up with 5 groups, so 5 is the answer.
If you devide any number into groups of 1, you will end up with the same number.
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Properties of Division: n/n =1, If n ≠ 0. Any number other than zero divided by itself is one.
1. Whenever you divide a number by itself, the answer is 1, except when dividing by zero.
Any real number (besides zero) divided by itself is equal to 1. In algebraic terms, if x is a non-zero real number then x/x=1. Zero is the exception because dividing a number by zero is undefined. For example 5 divided by itself is 1. 5/5=1
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Think of it this way...how many times can you divide a number by itself? The answer is always once. 4 divided by 4 equals 1. Using the number 4, 8 divided by 4 equals 2. In other words, 8 is equal to two 4s, right? But one 4 is always one 4.