High School Algebra 1 Properties of Equality notes and worksheets with examples and practice problems.

Let’s solve the problems shown in the worksheet step by step.

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First, look at the Commutative Property section:

It says:
> When adding or multiplying, the ________ does not matter.

We know from math that for addition and multiplication, you can switch the order of the numbers and still get the same result. For example:
- 2 + 3 = 5 and 3 + 2 = 5 → same answer
- 4 • 5 = 20 and 5 • 4 = 20 → same answer

So the missing word is order.

Now fill in the examples:
- 2 + 3 = 5
- 3 + 2 = 5
- 4 • 5 = 20
- 5 • 4 = 20

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Next, the Identity Property section:

It says:
> The sum of any number and ______ is that number.
> The product of any number and ______ is that number.

For addition: If you add 0 to any number, it stays the same. Example: 7 + 0 = 7 → so first blank is 0

For multiplication: If you multiply any number by 1, it stays the same. Example: 8 • 1 = 8 → so second blank is 1

Also given:
> 8 • 1 = 8

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Then, Additive Inverse:

It says:
> Sum of any number and negative of that number is ______.

Example: 5 + (-5) = 0 → always gives zero.

So the blank should be 0

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Final Answer:

Commutative Property blank: order
Examples:
2 + 3 = 5
3 + 2 = 5
4 • 5 = 20
5 • 4 = 20

Identity Property blanks:
Sum with 0
Product with 1
8 • 1 = 8

Additive Inverse: sum is 0