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

• A) 10, - 4/5• B) -3, -2• C) 3/2, 2/3• 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

• Commutativea + b = b + a

• Associative (a + b) + c = a + (b + c)

• Identitya + 0 = a, 0 + a = a

• Inversea + (-a) = 0

• Key Words; addition, sum

Multiplication

• Commutativeab = ba

• Associative(ab)c = a(bc)

• Identity a(1) = a

• Inversea(1/a) = 1 (a cannot = 0)

• Key words; product

Subtraction/Division

• Subtraction is just like adding; just add the oppositea – 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

• A) 3 + 5 = 5 + 3• B) 3 x 1 = 3• C) 4 + 0 = 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.

A) What is the sum of 4 and 21?B) What is the product of 10 and -6?C) What is the quotient of 7 and 1?

• Assignment• Pg. 6• #4-7, 15-19, 25-35 odd, 39-41, 43-49 odd, 51-

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