6 Math Connects, Course 3

Copyright ©

Glencoe/M

cGraw

-Hill, a division of T

he McG

raw-H

ill Com

panies, Inc.

A variable is a , usually a letter, used to

represent a .

An algebraic expression contains a , a

number, and at least one symbol.

When you substitute a number for the , an

algebraic expression becomes a numerical expression.

To evaluate an expression means to fi nd its

value.

To avoid confusion, mathematicians have agreed on a

called the order of operations.

BUILD YOUR VOCABULARY (pages 2–3)

EXAMPLES Evaluate Algebraic Expressions

Evaluate each expression if q = 5, r = 6, and s = 3.

4 (r - s) 2

4 (r - s) 2

= 4 ( - ) 2

Replace with 6 and

with 3.

= 4 ( ) 2

Perform operations in the

fi rst.

= 4 � Evaluate the .

= Simplify.

MAIN IDEA

• Evaluate expressions and identify properties.

1–2 Variables, Expressions, and Properties

KEY CONCEPT

Order of Operations

1. Do all operations within grouping symbols fi rst; start with the innermost grouping symbols.

2. Evaluate all powers before other operations.

3. Multiply and divide in order from left to right.

4. Add and subtract in order from left to right.

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1–2

Math Connects, Course 3 7

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a d

ivis

ion

of T

he M

cGra

w-H

ill C

ompa

nies

, Inc

.

Expressions such as 7 2 and 2 3 are called powers and

represent repeated .

BUILD YOUR VOCABULARY (pages 2–3)

q 2 - 4r - 1

q 2 - 4r - 1 = 4 - 4 - 1 Replace with 5 and

with 6.

Evaluate before

other operations.

.

Add and subtract in order from left to right.

.

= - 4(6) - 1

= 25 - - 1

= -

=

6q

_ 5s

The fraction bar is a grouping symbol. Evaluate the expressions in the numerator and denominator separately before dividing.

6q

_ 5s

= 6 (5) _

5 (3) Replace with 5 and with 3.

= 30 _ 15

Do all fi rst.

= .

Check Your Progress Evaluate each expression.

a. 2 (a + b) 2 if a = 3 and b = 2

b. b 2 + 3c - 5 if b = 4 and c = 2

c. 3s _ q + 4

if q = 2 and s = 4

001-031_CH01_881084.indd 7001-031_CH01_881084.indd 7 11/19/07 12:09:35 PM11/19/07 12:09:35 PM

1–2

8 Math Connects, Course 3

Copyright ©

Glencoe/M

cGraw

-Hill, a division of T

he McG

raw-H

ill Com

panies, Inc.

The branch of mathematics that involves with variables is called algebra.

Properties are sentences that are true for any numbers.

A counterexample is an example that shows that a

conjecture is .

BUILD YOUR VOCABULARY (pages 2–3)

REMEMBER IT Commutative Property

a + b = b + aa · b = b · a

Associative Property

a + (b + c) = (a + b) + ca · (b · c) = (a · b) · c

Distributive Property

a (b + c) = ab + aca (b - c) = ab - ac

Identity Property

a + 0 = aa · 1 = a

EXAMPLES Identify Properties

Name the property shown by 12 · 1 = 12.

Multiplying by 1 does not change the number.

This is the Property of Multiplication.

Check Your Progress Name the property shown by 3 · 2 = 2 · 3.

EXAMPLES Find a Counterexample

State whether the following conjecture is true or false.If false, provide a counter example.

The sum of an odd number and an even number is always odd.

This conjecture is .

Check Your Progress State whether the following conjecture is true or false. If false, provide a counterexample.

Division of whole numbers is associative.

HOMEWORKASSIGNMENTPage(s):

Exercises:

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