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Editor’s collection of notes:
Pre-Algebra
Property, Identity: Addition, Multiplication, Subtraction, Division
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What Is the Identity Property?
An identity is a number that when added, subtracted, multiplied or divided with any number (let's call this number n), allows n to remain the same. The identity will be either 0 or 1, depending on the operation that we are using. In addition and subtraction, the identity is 0. In multiplication and division, the identity is 1. That means that if 0 is added to or subtracted from n, then n remains the same. Also, if n is multiplied or divided by 1, then n remains the same.
Why Are the Identities Always 0 and 1?
It was mentioned before that the identity is always 0 for addition and subtraction and 1 for multiplication and division. Why is this, you may ask? Let's look deeper at how the operations actually work!
Addition is the process of adding something to something else. So when you add 7 to 0, you're going to get 7.
Subtraction is the process of taking away one amount from another amount. So when you subtract 0 from 7, you're going to get 7.
Multiplication is the process of repeated addition. When you multiply a number with another, you are repeatedly adding a number by the number of times stated by the other number. So, if you have 7 * 8, you are repeatedly adding the number 7 eight times. The identity of multiplication is 1, so if you have 7 * 1, you are repeatedly adding 7 one time. That gives us 7.
Division is the process of separating a number into parts. So if we have 7/1, we are separating the number 7 into one part. That would be 7, right? Yes!
If you were to substitute in any other number for 0 or 1 in the above scenarios, the math wouldn't work, which is why the identities are always 0 or 1.
These properties become important later when working on equations.
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