Honors Algebra Real Numbers and Real Operations Objectives: 1.Know the categories of numbers 2.Know where to find real numbers on the number line 3.Know the properties and operations of real numbers

…., -4, -3, -2, -1, 0, 1, 2, 3, 4,… counting numbers

…., -4, -3, -2, -1, 0, 1, 2, 3, 4,… counting numbers whole numbers

…., -4, -3, -2, -1, 0, 1, 2, 3, 4,… counting numbers whole numbers integers

rational numbers - numbers that can be written as a fraction or a decimal that repeats or terminates. Examples? irrational numbers - numbers that can’t be written as a fraction or a decimal that repeats or terminates. Examples?

Locate these numbers on a number line: 1.Approximate to decimal 2.Determine range and mark line 3.Plot original values

propertyadditionmultiplication closurea + b = real numberab = real number

propertyadditionmultiplication closurea + b = real numberab = real number commutative

propertyadditionmultiplication closurea + b = real numberab = real number commutativea + b = b + a

propertyadditionmultiplication closurea + b = real numberab = real number commutativea + b = b + aab = ba

propertyadditionmultiplication closurea + b = real numberab = real number commutativea + b = b + aab = ba associative

propertyadditionmultiplication closurea + b = real numberab = real number commutativea + b = b + aab = ba associative(a + b) + c = a + (b + c)

propertyadditionmultiplication closurea + b = real numberab = real number commutativea + b = b + aab = ba associative(a + b) + c = a + (b + c)(ab)c = a(bc)

propertyadditionmultiplication closurea + b = real numberab = real number commutativea + b = b + aab = ba associative(a + b) + c = a + (b + c)(ab)c = a(bc) identity

propertyadditionmultiplication closurea + b = real numberab = real number commutativea + b = b + aab = ba associative(a + b) + c = a + (b + c)(ab)c = a(bc) identitya + 0 = a

propertyadditionmultiplication closurea + b = real numberab = real number commutativea + b = b + aab = ba associative(a + b) + c = a + (b + c)(ab)c = a(bc) identitya + 0 = aa x 1 = a

propertyadditionmultiplication closurea + b = real numberab = real number commutativea + b = b + aab = ba associative(a + b) + c = a + (b + c)(ab)c = a(bc) identitya + 0 = aa x 1 = a inverse

propertyadditionmultiplication closurea + b = real numberab = real number commutativea + b = b + aab = ba associative(a + b) + c = a + (b + c)(ab)c = a(bc) identitya + 0 = aa x 1 = a inversea + -a = 0

propertyadditionmultiplication closurea + b = real numberab = real number commutativea + b = b + aab = ba associative(a + b) + c = a + (b + c)(ab)c = a(bc) identitya + 0 = aa x 1 = a inversea + -a = 0a x 1/a = 1

propertyadditionmultiplication closurea + b = real numberab = real number commutativea + b = b + aab = ba associative(a + b) + c = a + (b + c)(ab)c = a(bc) identitya + 0 = aa x 1 = a inversea + -a = 0a x 1/a = 1 distributive

propertyadditionmultiplication closurea + b = real numberab = real number commutativea + b = b + aab = ba associative(a + b) + c = a + (b + c)(ab)c = a(bc) identitya + 0 = aa x 1 = a inversea + -a = 0a x 1/a = 1 distributivea(b + c) = ab + ac opposite of a = -a Inverse of a = 1/a

propertyadditionmultiplication closurea + b = real numberab = real number commutativea + b = b + aab = ba associative(a + b) + c = a + (b + c)(ab)c = a(bc) identitya + 0 = aa x 1 = a inversea + -a = 0a x 1/a = 1 distributivea(b + c) = ab + ac Identify the property: = (3 ● 5) = (2 ● 3)5 3. 4(3 + 7) = 4 ● ● = (x + 5) + 4 = x + (5 + 4) 6. 1x = x 7. 3 ● 1/3 = ● 3 ● 4 = 3 ● 2 ● 4

Honors Algebra Algebraic Expressions and Models Objectives: 1.Evaluate algebraic expressions 2.Simplify expressions 3.Apply expressions to real world examples

Vocabulary: power – a number and it’s exponent Vocabulary: power base exponent 5252

Vocabulary: power – a number and it’s exponent Vocabulary: power 5252 =5∙5 5 to the second power 5 squared

Vocabulary: power – a number and it’s exponent Vocabulary: power 5353 =5∙5∙5 5 to the third power 5 cubed

∙3∙3∙3 2∙2∙2∙2∙2 9∙9∙9 1∙1∙1∙1∙1∙1 3 to the fourth power 2 to the fifth power 9 cubed (to the 3 rd power) 1 to the sixth power to the 4 th power 4 7

Please Excuse My Dear Aunt Sally P – parenthesis E – exponents M – multiplication D – division A – addition S – subtraction Left to Right

P – parentheses and other grouping symbols from left to right E – exponents from L to R M – multiplication/division from L to R A – addition/subtraction from L to R Please Excuse My Aunt

Evaluate these expressions:

Evaluate when x = 2 when x = 2/ /3 **Calculator Tip : Decimal  Fraction Math, >Frac

Like terms – terms that have the same variables with the same powers

Simplify these expressions:

Real World Applications See Note Sheet…

You have 122 dollars from bagging at Dominick’s and you want to buy some DVD’s. If each DVD cost $13, write an expression to represent the amount of money you have left buying in DVD’s.

You want to buy either scented lotion or bath soap for 8 people. The lotions are $6 for each and the soaps are $5 each. Write and expression for the total amount you must spend. Evaluate the expression when 5 people get the lotion.

Write an expression for the total amount of juice in 15 cans if some hold 8 oz and some hold 12 oz. What is the total if 9 of the cans hold 8 oz?

Practice…Try These on the Back

HMWK! Worksheet : #s 7-15, 13-24

Today’s Agenda! Collect Signed Syllabus Return Syllabus Scavenger Hunt HW Questions/Concerns Section 1.3 Notes –1.3 Domino Worksheet Word Problems HA2 Pretest Tomorrow! (Bring #2 Pencil)

Honors Algebra Solving Linear Equations Objectives: 1.Solve simplified linear equations 2.Solve linear equations that need simplifying 3.Solve linear equation from real life Vocabulary: solution, equation, identity equation, inconsistent equation

PEMA – used to evaluate an expression

Rules for Solving an Equation 1.Distribute 2.Combine Like Terms 3.Move variable to one side 4.Isolate variable using inverse operations 5.Check

Solving an equation – working backwards

(4/5)(x – 2) = 16

2x + 5 = 7x – 16 3(x – 7) + 2x = -5(2x – 4) 2x + 8 = 5x – 2(x – 8)

Infinite Solutions/No Solutions 4x – 3 = 2(2x – 9) + 4 7x + 5 – 3x = -8x x

Domino WKST!

Real World Applicaiton See Note Sheet…

Katie works at a restaurant. She earns $3 per hour base plus tips. She averages $12 in tip per hour. How many hours until she has earned $333? 22.2 hours

A car salesman base salary is $21,000 plus 5% commission on sales. How much must he sell to earn $65,000. $880,000 of cars

The bill from your plumber is $134. The cost for labor was $32 per hour. The cost for material was $46. How many hours did the plumber work? 2.75 hours

Honors Alg 2 The perimeter of a triangle is 35 feet. If the sides are 3x – 5, 2x – 3, and 15-x, what are its dimensions? x = 7 sides of 16, 13, and 8 units

Assignment: WS 1.1-3, #11-23 on backside Honors Alg 2