# Write a number sentence that shows the commutative property of addition

Rearrange, using the Associative Property: 2 3x They want me to regroup things, not simplify things.

What gives? These are all going to add up to the same things, and it makes sense.

Use the Distributive Property to rearrange: 4x — 8 The Distributive Property either takes something through a parentheses or else factors something out. Since there aren't any parentheses to go into, you must need to factor out of.

## Commutative property multiplication

Associative Property Affiliate The word "associative" comes from "associate" or "group"; the Associative Property is the rule that refers to grouping. The easiest one to find the sum of-- actually, let's do all of them. Why is the following true? But the easiest one, just because a lot of people immediately know that 5 plus 5 is 10, is to maybe start with the 5 plus 5. In this case, they do want me to simplify, but I have to say why it's okay to do Any time they refer to the Associative Property, they want you to regroup things; any time a computation depends on things being regrouped, they want you to say that the computation uses the Associative Property. While the topic will start to become relevant in matrix algebra and calculus and become amazingly important in advanced math, a couple years after calculus , they really don't matter a whole lot now. This is one of those times when it's best to be flexible. What gives? Don't worry about their "relevance" for now; just make sure you can keep the properties straight so you can pass the next test. Now, they say in a different way, and then find the sum.

This is one of those times when it's best to be flexible. In the latter case, it's easy to see that the Distributive Property applies, because you're still adding; you're just adding a negative.

The lesson below explains how I keep track of the properties. Up here, 5 plus 8 is Any time they refer in a problem to using the Distributive Property, they want you to take something through the parentheses or factor something out ; any time a computation depends on multiplying through a parentheses or factoring something outthey want you to say that the computation used the Distributive Property.

## Commutative property definition

The lesson below explains how I keep track of the properties. These are all going to add up to the same things, and it makes sense. Associative, Commutative, and Distributive Properties Basic Properties Other Properties Purplemath There are three basic properties of numbers, and your textbook will probably have just a little section on these properties, somewhere near the beginning of the course, and then you'll probably never see them again until the beginning of the next course. We could order it as 5 plus 5 plus 8. Now, let's verify that these two are the same exact thing. Since all they did was regroup things, this is true by the Associative Property. If I have 5 of something and then I add 8 more and then I add 5 more, I'm going to get the same thing as if I had took 5 of something, then added the 5, then added the 8. The other two properties come in two versions each: one for addition and the other for multiplication. You could try all of these out. Any time they refer in a problem to using the Distributive Property, they want you to take something through the parentheses or factor something out ; any time a computation depends on multiplying through a parentheses or factoring something out , they want you to say that the computation used the Distributive Property. Up here, 5 plus 8 is Don't worry about their "relevance" for now; just make sure you can keep the properties straight so you can pass the next test. Content Continues Below Commutative Property The word "commutative" comes from "commute" or "move around", so the Commutative Property is the one that refers to moving stuff around. If we go down here, 8 plus 5 is

They want me to move stuff around, not simplify. Advertisement "But wait! Distributive Property Affiliate The Distributive Property is easy to remember, if you recall that "multiplication distributes over addition".

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