There are four basic properties of numbers: commutative, associative, distributive, and identity. You should be familiar with each of these. It is especially important to understand these properties once you reach advanced math such as algebra and calculus.

a. **Addition**. When two numbers are added, the sum is the same regardless of the order in which the numbers are added.

3 + 5 = 8 or 5 + 3 = 8

b. **Multiplication**. When two numbers are multiplied together, the product is the same regardless of the order in which the numbers are multiplied.

3 x 5 = 15 or 5 x 3 = 15

a. **Addition**. When three or more numbers are added, the sum is the same regardless of the way in which the numbers are grouped.

6 + (4 + 3) = 13 or (6 + 4) + 3 = 13

b. **Multiplication**. When three or more numbers are multiplied, the product is the same regardless of the way in which the numbers are grouped.

6 x (4 x 3) = 72 or (6 x 4) x 3 = 72

The sum of two numbers times a third number is equal to the sum of each addend times the third number.

5 x (7 + 2) = 45 or 5 x 7 + 5 x 2 = 45

a. **Addition**. The sum of any number and zero is that number.

12 + 0 = 12

b. **Multiplication**, The product of any number and one is that number.

18 x 1 = 18

Knowing these properties of numbers will improve your understanding and mastery of math.

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