The identity numbers for addition and multiplication
What are identity numbers?
Identity numbers are numbers that don’t change the “identity” of the original value.
The identity for addition is ???0???.
The identity for multiplication is ???1???.
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The reason is that
You can add ???0??? to any number and it doesn’t change the original value.
You can multiply any number by ???1??? and it doesn’t change the original value.
How identity numbers leave the identity unchanged
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The identity numbers for addition and multiplication
Example
What is ???17+0????
Without even thinking about this in terms of identity numbers, we should already know that ???17+0=17???, because if you have ???17??? and you add nothing to it, you still have ???17???.
If we think about this more technically in terms of identity numbers, we know that ???0??? is the identity number for addition. Since we are adding ???0???, and because ???0??? is the identity number for addition, we know that adding ???0??? to ???17??? won’t change the identity of ???17???, so ???17+0??? will just be ???17???.
Let's look at an example with the identity number for multiplication.
Identity numbers are numbers that don’t change the “identity” of the original value.
Example
What is ???4\times1????
In this problem we’re multiplying ???4??? by ???1???. We should already know that ???4??? times ???1??? is just ???4???, and we don’t really need identity numbers to tell us this.
But the identity number concept confirms that this is true. We know that ???1??? is the identity number for multiplication. Since we are multiplying by ???1???, and because ???1??? is the identity number for multiplication, we know that multiplying ???4??? by ???1??? won’t change the identity of ???4???, so ???4\times1??? will just be ???4???.
