Chapter 1 Review
Foundations

# Chapter 1 Vocabulary

Learning vocabulary is an extremely important part of studying the math language. Much of the author's meaning is lost if the student doesn't understand the implications of a chosen word. Use the following tools to practice the vocabulary from Chapter 1.

 Number Properties Sets of Numbers

# Compare Numbers

For any two real numbers a and b, a is greater than b if a is to the right of b on a number line.

Skill Check

# Simplify Fractions

To simplify fractions, divide out the greatest factor that is common to the numerator and denominator.

Skill Check

# Integer Operations

If the signs are the same, keep the sign and add the numbers.  If the signs are different, subtract the numbers and give the answer the sign of the larger number

Subtract:

Change the subtraction to addition and write the opposite of the number that comes after i

Multiply/Divide:

Two negatives give a positive answer; a positive and a negative give a negative answer.

Skill Check 1

Skill Check 2

Skill Check 3

Skill Check 4

Skill Check 5

# Fraction Operations

**Always reduce the answer to lowest terms.  Unless otherwise stated, leave the answer as an improper fraction rather than changing it to a mixed fraction.**

Find a common denominator.  Add/Subtract the numerators.  Keep the denominator.

Multiply:

Reduce any common factors in the numerator and denominator.  Then multiply the numerators together and the denominators together.

Divide:

Leave the first fraction the way it is; change divide to times; write the reciprocal of (flip) the second fraction.

Try these:

# Exponents and Roots

Even powers of negative numbers

Be very careful to distinguish between these problems. The placement of the parentheses makes a difference!

Base

Exponent

Evaluate

32

3

2

(3)(3) = 9

(- 3)2

- 3

2

(- 3)(- 3) = 9

- (3)2

3

2

- (3٠3) = - 9

- 32

3

2

- (3٠3) = - 9

These will cause problems when you are evaluating expressions so be careful.  If you are using a calculator, you must enter them correctly or the calculator will give you a wrong answer.  Experiment with your calculator to be sure you can do it correctly.

Skill Check 1

Skill Check 2

Skill Check 3

Skill Check 4

# Order of Operations

Groups

These can be parentheses, brackets, absolute value bars, radicals, fraction numerator, or fraction denominator.

Powers and Roots

Evaluate any exponential expressions or radicals.

Multiply/Divide

Multiplication and division have the SAME level of importance.  If both appear in a problem, work them from left to right.

Addition and subtraction have the SAME level of importance.  If both appear in a problem, work them from left to right.

Try these. Be sure to ask questions, if you have trouble getting the correct answer.

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

# Evaluating expressions

When evaluating expressions, rewrite the problem and put (  ) where there is a variable.  Then fill in the parentheses with the given value for the variable.  Remember the order of operations!

Try these.

Problem 1

Problem 2

# Undefined Expressions

An expression is undefined any time the denominator is equal to 0.

Skill Check 1

Skill Check 2

# Combining like terms

Add or subtract the coefficients of terms that have the same variable. Remember the sign stays with the number that comes after it.