Commutative property of addition

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

Try the following examples to help you learn faster.

Addition Commutative Property

Other relevant addition properties

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

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