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1.1 – Real Numbers, Number Operations

Most things in math and life we work with are real numbers
We can divide real numbers into two categories; Rational Irrational

Rational vs. Irrational
Rational = a number that may be written as a ratio of integers AND decimals that terminate or repeat Types of Rational Numbers 1) Integers (no decimals, positive and negatives); -27, 3, 0, 45 2) Whole Numbers (no decimals, only zero and positives); 0, 1, 2,…, 100

Irrational Irrational = cannot be written as ratio of integers AND decimals that terminate/repeat Most common irrational number? Others; √2, √14

Real Numbers on Number Line
Recall from Algebra 1, we can represent the real numbers and their values using a number line On a number line, we use “0” as a place marker; negatives to the left, positives to the right

Example. Plot the following numbers on a number line.
-2/5, 5, 10, 0, -2

Comparing Real Numbers
With real numbers, we can compare their values using inequality symbols Read an inequality like you read a book; left to right < = less than > = greater than ≥ = greater than OR equal to ≤ = less than OR equal to

Example. Compare the following pairs of numbers using one of the four inequality symbols
D) 0, 50

Example. Graph the following numbers on a number line, then put them in order from least to greatest. -6, 3, -3, 4, -14, 0, 9

Addition and Multiplication Properties
With the real numbers, we have several properties for addition and multiplication You use these all the time, but probably forgot their “technical” names

Addition Commutative Associative Identity Inverse a + (-a) = 0
a + b = b + a Associative (a + b) + c = a + (b + c) Identity a + 0 = a, 0 + a = a Inverse a + (-a) = 0 Key Words; addition, sum

Multiplication Commutative Associative Identity a(1) = a Inverse
ab = ba Associative (ab)c = a(bc) Identity a(1) = a Inverse a(1/a) = 1 (a cannot = 0) Key words; product

Subtraction/Division
Subtraction is just like adding; just add the opposite a – b = a + (-b) Key words; difference Division is multiplication by the reciprocal a/b = a(1/b) Key words; quotient

Example. Identify the following properties
B) 3 x 1 = 3 C) = 4 D) (6 x 3) x 9 = 6 x (3 x 9) E) 4(9 + 2) = 4x9 + 4x2

Example. Perform the operation to answer the question.
What is the sum of 4 and 21? What is the product of 10 and -6? What is the quotient of 7 and 1?

Assignment Pg. 6 #4-7, 15-19, odd, 39-41, odd, 51-53

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