 # 1.1 – Real Numbers, Number Operations

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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

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