Download Section 1.3 and 1.4 Notes

Sections 1.3 and 1.4- Classifying Real Numbers, Properties of Real Numbers
Essential Question: Why are real number properties essential in algebra?
Do Now:
Classifying Real Numbers
Word Bank: Rational, Irrational, Whole, Integer and Natural
Fill in the chart below with one of the words along with a brief description and
examples of the subset of real numbers.
Create a diagram below showing the relationship between the subsets of real numbers.
Example 1: Critical Thinking Questions Involving Real Numbers
a. Give an example of a rational number that is NOT an integer.
b. Tell whether each square root is rational or irrational. Explain.
i) √100
ii) √0.29
Properties of Real Numbers

Commutative Properties- changing the __________________ does not affect final
answer
Think of the root word

Associative Properties- changing the ____________________ does not affect the
final answer
Think of the root word

Identity Properties- your result is the
_______________________________________
NOTE: These properties apply only to ____________________ and
___________________.
Example 2: Identifying Properties
What property is illustrated by each statement?
a. 4𝑥 ∙ 1 = 4𝑥
b. 𝑥 + (√𝑦 + 𝑧) = 𝑥 + (𝑧 + √𝑦)
Group Work:
Tell whether each statement is true or false. Explain.
1. All negative numbers are integers.
2. All integers are rational numbers.
3. All square roots are irrational numbers.
4. No positive number is an integer.
5.
Tell whether the expressions in each pair are equivalent. Briefly explain why.
6. 2 + ℎ + 4 and 2 ∙ ℎ ∙ 4
7. 𝑚(1 − 1) and 0
8. (3 + 7) + 𝑚 and 𝑚 + 10
9. (2+5−7) and 11𝑥
11𝑥
HW: p. 20-21 #29-36, 45, 46, 62; p. 26-28 #7-12, 52-55