Mary Jane Sterling - Algebra I All-in-One For Dummies

When you get to the three terms with subtraction and addition signs, , you always perform the operations in order, reading from left to right. (See Chapter 7for more on this process, called the order of operations.)

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A.You have to complete the work in the denominator first before dividing the 32 by that result:

As you’re working through the problems, just remember to:

Work from the inside out when there are several grouping symbols.

Move from left to right when performing addition and/or subtraction on several different terms.

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Three important processes in algebra are the distributive property, the associative property, and the commutative property. Because some operations have these properties, it makes working with the variables and numbers so much easier and nicer.

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.

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A.Distribute the 3 over the by multiplying each term by 3: . Then simplify the terms: .

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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.

The associative property means that even if a particular grouping of the operation changes, the result remains the same. (If you need a reminder about grouping, refer to the section, “ Getting a Grip on Grouping Symbols,” earlier in this chapter.) Addition and multiplication are associative operations. Subtraction and division are not associative. So,

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 , the property seems to work. Also, in the division problem , it seems to work. I just picked numbers very carefully that would make it seem like you could associate using subtraction and division. Although there are exceptions, a rule must work all the time, not just in special cases.