The Commutative Property Of Addition

The Commutative Property Of Addition is perhaps the easiest of the math concepts to explain of all.

1 plus 2 is the same as 2 plus 1. It doesn't matter what order you add them in, they are the same. This comes up in talks about order of operation. PEMDAS.

Which do you add first?

Doesn't matter...just make sure you do everything but subtraction first...

Base ten blocks, 12 x 13

I'll add more to this page later.

Spend less time fooling with the definitions and more time fooling with the blocks. DO addition.

"More time doing less time talking," as they say.


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Go from Commutative Property Of Addition to the The Associative Property of Addition.

“Math illiteracy strikes 8 out of 5 people.”

“The whole is more than the sum of the parts.” Aristotle (384-322 BC)

The Four Properties of Addition

There are four properties of addition: they 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 3 + 2 = 2 + 3Algebraic: x + y = y + x

Associative Property: When three or more numbers are added, the sum is the same regardless of the order of addition.

The property states that for all real numbers a, b, and c, their sum is always the same, regardless of their grouping:

(a + b) + c = a + (b + c)

For example (1 + 2) + 3 = 1 + (2 + 3)Algebraic: (x + y) + z = x + (y + z)

Additive Identity Property: The sum of any number and zero is the original number.

For example 1 + 0 = 5.Algebraic: x + 0 = x (Crucially important concept especially when you understand 0 = x - x. Hero zero! Helps solve equalities.

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)
Algebraic: x(y + z) = xy + xz