, Chapter 1
Prerequisites
1.1 Real Numbers: Algebra Essentials
Section Exercises
Verbal
1. Is an example of a rational terminating, rational repeating, or irrational number? Tell
why it fits that category.
Irrational number. The square root of two does not terminate, and it does not repeat a
pattern. It can’t be written as a quotient of two integers, so it is irrational.
2. What is the order of operations? What acronym is used to describe the order of
operations, and what does it stand for?
The order of operations is a set of rules that prioritize the different operations such that
expressions can be evaluated consistently. PEMDAS stands for Parentheses, Exponents,
Multiplication and Division, Addition and Subtraction.
3. What do the Associative Properties allow us to do when following the order of
operations? Explain your answer.
The Associative Properties state that the sum or product of multiple numbers can be
grouped differently without affecting the result. This is because the same operation is
performed (either addition or subtraction), so the terms can be re-ordered.
Numeric
For the following exercises, simplify the given expression.
4.
5.
,6.
7.
8.
9.
10.
11.
12.
13.
, 14.
15.
16.
17.
18.
19.
20.
21.
Prerequisites
1.1 Real Numbers: Algebra Essentials
Section Exercises
Verbal
1. Is an example of a rational terminating, rational repeating, or irrational number? Tell
why it fits that category.
Irrational number. The square root of two does not terminate, and it does not repeat a
pattern. It can’t be written as a quotient of two integers, so it is irrational.
2. What is the order of operations? What acronym is used to describe the order of
operations, and what does it stand for?
The order of operations is a set of rules that prioritize the different operations such that
expressions can be evaluated consistently. PEMDAS stands for Parentheses, Exponents,
Multiplication and Division, Addition and Subtraction.
3. What do the Associative Properties allow us to do when following the order of
operations? Explain your answer.
The Associative Properties state that the sum or product of multiple numbers can be
grouped differently without affecting the result. This is because the same operation is
performed (either addition or subtraction), so the terms can be re-ordered.
Numeric
For the following exercises, simplify the given expression.
4.
5.
,6.
7.
8.
9.
10.
11.
12.
13.
, 14.
15.
16.
17.
18.
19.
20.
21.
