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Chapter 2

Recognizing Algebraic Properties and Notation

The properties used in mathematics were established hundreds of years ago. Mathematicians around the world wanted to be able to communicate with one another; more specifically, they wanted to get the same answers when working on the same questions. To help with that, they developed and adopted rules such as the commutative property of addition and multiplication, the associative property of addition and multiplication, and the distributive property.

The Problems You’ll Work On

To strengthen your skills with algebraic properties and notation, you’ll practice doing the following in this chapter:

 Using the distributive property of multiplication over addition and subtraction

 Paying attention to the order of operations

 Simplifying radicals and radical expressions

 Reassociating terms for easier computation

 Regrouping and commuting for ease and accuracy

What to Watch Out For

Here are a few things to keep in mind while you work in this chapter:

 Distributing a negative number over several terms and being sure to apply the negative sign to each term

 Recognizing the fraction line as a grouping symbol

 Performing the absolute value operation when it’s used as a grouping symbol

 Applying the correct exponent when multiplying or dividing variables

Applying Traditional Grouping Symbols

51–58 Simplify the expressions.

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Introducing Some Non-Traditional Grouping Symbols

59–64 Simplify the expressions involving radicals and absolute value.

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Distributing Multiplication over Addition and Subtraction

65–72 Perform the distributions over addition and subtraction.

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Associating Terms Differently with the Associative Property

73–78 Use the associative property to simplify the expressions.

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Rearranging with the Commutative Property

79–84 Use the commutative property to simplify the expressions.

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Applying More Than One Property to an Expression

85–90 Simplify each expression using the commutative, associative, and distributive properties.

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