Sect. 1.2 Operations & Properties of Real Numbers  Absolute Value  Inequalities  Addition, Subtraction, Opposites  Multiplication, Division, Reciprocals  Laws: Commutative, Associative, Distributive 11.2

Absolute Value – Concept  Positive distance from 0 on a number line  How far is the number 6 from the 0 point?  6 units  How far is from the 0 point?  4.75 units 21.2

Absolute Value – Notation 31.2

Inequalities – Concept  Use the number line to understand  < less than  > more than  Express the relation of -4 to -7 Either -7 < -4 or -4 > -7 both ways are correct 41.2

Addition of any Two Numbers 51.2

Opposites (Additive Inverses) 61.2

Opposites and Absolute Value  Opposites are a pair of numbers that sum to and /17 and 3/17 0 and 0 (zero is it’s own opposite)  The Absolute Value of a number is the positive value of it’s pair of opposites |11.2| = 11.2 and |-11.2| = 11.2 |-3/17| = 3/17 and |3/17| = 3/17  Absolute value brackets can hold expressions |3 – 5| = |-2| = 2 |5 – 3| = |2| = 2 -|22| = -22 and -|-22| =

Multiplication & Division (+ or – ?) 81.2

Fractions with One Negative Sign These are the Simplest Forms 91.2

The Law of Reciprocals What is 4’s reciprocal? ¼ because 4 (¼) = 1 What is 3½ ’s reciprocal? 2/7 Because (7/2)(2/7) = 1 a and 1/a are Multiplicative Inverses 101.2

Division by Zero 111.2

Another look at Grouping Symbols and the Order of Operations 121.2

Equivalent Expressions  Two expressions are Equivalent when they have the same values for all possible replacements  Are the following two expressions equivalent? 3x + 4 and x – 3 + 2x + 7  Yes – when simplified, the 2 nd expression matches the 1 st 131.2

I Must Remember: Commutative  An operation is Commutative when Two values can switch positions, and the result is the same.  COMMUTATIVE  Addition and Multiplication are Commutative = 17 7(9) = = 17 9(7) = 63  Are Subtraction or Division Commutative ? 141.2

Commutative Laws 151.2

I Must Remember: Associative  Three values can be computed in different order and the result is the same. (same operations)  ASSOCIATIVE ASSOCIATIVE  Addition and Multiplication are Associative (19 + 4) + 6 = = 29 (3)(7)(5) = 21(5) = (4 + 6) = = 29 (3)(7)(5) = 3(35) = 105  Are Subtraction or Division Associative ? 161.2

The Associative Laws 171.2

The Distributive Law and (a + b)c = ac + bc 181.2

Let’s play Name That Law!  x y = x + y + 5 Commutative … COM  3a + 6 = 3(a + 2) Distributive … DIST  7x(1 / x) = 7 Reciprocals … RECIP  (x + 5) + y = x + (5 + y) Associative … ASSOC  4(a + 2b) = 8b + 4a COM, then DIST or DIST, then COM 191.2

Let’s look at next time …  Section 1.3 Solving Equations Section 1.3  If we have time today, let’s review Reducing Numeric Fractions 201.2