When an estate is “distributed,” everyone hopes to get an equal share. The distributive property works the same way. The distributive property is used when you perform an operation on each of the terms within a grouping symbol. The following rules show distributing multiplication over addition and distributing multiplication over subtraction:
The distributive property is frequently employed when terms within parentheses or other grouping symbols cannot be combined. This allows for each term to interact with the multiplier.
A. Distribute the 3 over the
Q.
A.
7
8
9
10
11
12
Making Associations Work
The associative property has to do with grouping — that is, how you deal with two or more terms when you perform operations on them. Think about what the word associate means. When you associate with someone, you’re close to the person, or you’re in the same group with them. Say that Anika, Becky, and Cora associate. Whether Anika drives over to pick up Becky and the two of them go to Cora’s house and pick her up, or Cora is at Becky’s house and Anika picks up both of them at the same time, the same result occurs: all three are in the car at the end.
You can always find a few cases where the associative property works even though it isn’t supposed to. For example, in the subtraction problem
Here’s how the associative property works:
A. With the current grouping, you need to add
Q. Use the associate property to create an easier problem:
A. Regroup, putting the first two numbers together:
13
14
15
16
Computing by Commuting
Before discussing the commutative property, take a look at the word commute. You probably commute to work or school and know that whether you’re traveling from home to work or from work to home, the distance is the same: The distance doesn’t change because you change directions (although getting home during rush hour may make that distance seem longer).
The same principle is true of some algebraic operations: It doesn’t matter whether you add
