## Trying to master Commutative property of addition

### Definition: (a + b) + c  =  a + (b + c)

The word “commutative” comes from “commute” or “move around”, so the Commutative Property is the one that refers to moving stuff around. For addition, the rule is “a + b = b + a”; in numbers, this means 2 + 3 = 3 + 2. For multiplication, the rule is “ab = ba”; in numbers, this means 2×3 = 3×2.

### Easy to Remember Trick

Why “commutative” … ?

Because the numbers can travel back and forth like a commuter.

The word “commutative” comes from “commute” or “move around”, so the Commutative Property is the one that refers to moving stuff around. For addition, the rule is “a + b = b + a“; in numbers, this means 2 + 3 = 3 + 2. For multiplication, the rule is “ab = ba“; in numbers, this means 2×3 = 3×2. Any time they refer to the Commutative Property, they want you to move stuff around; any time a computation depends on moving stuff around, they want you to say that the computation uses the Commutative Property.

• #### Use the Commutative Property to restate “3×4×x” in at least two ways.

They want me to move stuff around, not simplify. In other words, my answer should not be “12x“; the answer instead can be any two of the following:

4 × 3 × x

4 × x × 3

3 × x × 4

x × 3 × 4

x × 4 × 3

### Practice

There are four mathematical properties which involve addition. The properties are the commutative, associative, additive identity and distributive properties.

Commutative property: When two numbers are added, the sum is the same regardless of the order of the addends. For example 4 + 2 = 2 + 4

Associative Property: When three or more numbers are added, the sum is the same regardless of the grouping of the addends. For example (2 + 3) + 4 = 2 + (3 + 4)

Additive Identity Property: The sum of any number and zero is the original number. For example 5 + 0 = 5.

Distributive property: The sum of two numbers times a third number is equal to the sum of each addend times the third number. For example 4 * (6 + 3) = 4*6 + 4*3

## Properties of Operations

You probably use properties of operations every day without even giving them a thought. You may have noticed that 3 x 4 and 4 x 3 are both 12. That”s an example of the commutative property of multiplication. The ideas are probably familiar – you just need to brush up on the vocabulary.

Let”s get started

The associative and commutative properties hold for both addition and multiplication.
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