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 for Pre-Algebra — 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 $4$ .