Basic Mathematics for College Students

696 Chapter 8 Summary and Review

CHAPTER 8 SUMMARY AND REVIEW

SECTION 8.1 The Language of Algebra

A variableis a letter (or symbol) that stands

for a number. Since numbers do not change

value, they are called constants.

DEFINITIONS AND CONCEPTS EXAMPLES

Variables: x, a,andy

Constants: 8, , 2 and 3.14

3

5

 10 ,

STUDY SKILLS CHECKLIST

Expressions and Equations

Before taking the test on Chapter 8, make sure that you know the difference between

simplifying an expression and solving an equation. Put a checkmark in the box if you can

answer “yes” to the statement.

I know that an expressiondoes not contain an =

symbol.

Expressions:

2 x 3 x 4(5y2)

I know how to simplify expressions by combining

like terms.

2 x 3 xis 5x

I know how to use the distributive property to

simplify expressions.

4(5y2) is 20y 8

I know that an equationcontains an = symbol.

Equations:

x 5  98 y 40

 

I know how to use the addition and subtraction

properties of equality to solve equations. If a

number is added to (or subtracted from) one side

of an equation, the same number must be added to

(or subtracted from) the other side.

x 5  9

x 5  5  9  5 Subtract 5 from both sides.

x 4

I know how to use the multiplication and division

properties of equality to solve equations. If the

one side of an equation is multiplied (or divided)

by a number, the other side must be multiplied

(or divided) by the same number.

8 y 40

Divide both sides by 8.

y 5

8 y

8



 40

8

When multiplying a variable by a number, or a

variable by another variable, we can omit the

symbol for multiplication.

Many of the properties that we have seen

while working with whole numbers, integers,

fractions, and decimals can be generalized and

stated in symbols using variables.

3 xmeans 3 xabmeans ab 4 rstmeans 4 rst

The Commutative Property of Addition

a+ b= b+ a

The Associative Property of Multiplication

(ab)c= a(bc)