BELL RINGER1-3 READING QUIZ 10-9

1. What is the Title of Lesson 1-3? 2. What are the names of the 3

properties associated with Multiplication?

3. What is the difference between the commutative and the associative property?4. What number is called the additive identity?

5. What number is called the multiplicative identity?

1-3 PROPERTIES OF NUMBERS OBJECTIVES

By the end of class, students will be able to: Recognize the properties of equality and

identity Recognize the commutative and

associative properties.with 90% or above mastery.

2 ADDITION PROPERTIES

Additive Identity – Any number plus 0 = the number. 0 is called the additive identity.

a + 0 = aExample: 2 + 0 = 2 Additive Inverse - Any number and

its opposite are additive inverses. Their sum = 0.

a + (-a) = 0Example: 100 + (-100) = 100 -

100 = 0

3 MULTIPLICATION PROPERTIES

Multiplicative Identity – The product of a number and 1 is the number.

a 1 = 1 a = aExample: 14 1 = 1 14 = 14 Multiplicative Inverse - A number

times its reciprocal is 1. a b = 1b a a, b 0

Example: 4 5 = 15 4

Multiplicative Property of 0 – The product of any number and 0 is 0.

a 0 = 0

Example: 9 0 = 0

Commutative Property - The order in which you add or multiply doesn’t change their sum or product.

a + b = b +aa(b) = b(a)

Example: 4 + 8 = 8 + 4 7(11) = 11(7)

Associative Property – Grouping numbers does not change the sum or product.

(a + b) + c = a + (b + c)Example: (3 + 5) + 7 = 3 + (5 + 7)

CLASSWORK P. 20 – 21IN TEAMS

Do 37, 39, 43, 45, 47, 57, 58 in your notebook

Now lets look at 14.

P. 19 #1414. 6 1 + 5(12 ÷ 4 – 3) 6

6 1 + 5(3 – 3) Substitution 6

6 1 + 5(0) Additive Inverse 6

1+ 5(0) Multiplicative Inverse

1 + 0 Multiplicative Property of 0

1 Additive Identity

4 PROPERTIES OF EQUALITY

Properties of Equality Reflexive Property–Any quantity is

equal to itself

a = aExample: 4 + 7 = 4 + 7

5 = 5 Symmetric Property – If one quantity

equals a second, then the second quantity equals the first.

If a = b, then b = a.Example: If 8 = 2 + 6, then 2 + 6 =

8.

4 PROPERTIES OF EQUALITY

Substitution Property – A quantity may be substituted for its equal in any expression. If a = b, then a can be replaced for its equal in any expressions.

Example: If n = 11, then 4n = 4(11).

Transitive Property – If one quantity equals a second quantity and the second quantity equals the third quantity, then the first quantity equals the third quantity.

If a = b and b = c, then a = c

Example: If 6 + 9 = 3 + 12 and 3 + 12 = 15,

6 + 9 = 15

PROPERTIES OF EQUALITY

Do p. 31 60, 62

DO P. 19-20 16, 29, 51

16. Hotel Rates: Important FactsMon - Fri $72, Tax $5.40Sat, Sun $63, Tax $5.10

2(72) + 2(5.10) + 2(63) + 2(5.40)144 + 10.20 + 126 + 10.80(144 + 126) + (10.20 + 10.80)270 + 21 = 291The total cost of the room including tax

$291.

P. 20 #29 29. Scuba DrivingExpression 1: 2($10.95) + 3($7.50) + 2($5.00) +

5(418.99) = $21.90 + $22.50 + $10 + $94.95

$149.35The total sales are $149.35.Expression 2: 2($10.95 + $5) + 3($7.50) + 5($18.99) 2($15.95) + $22.50 + $94.95

$31.90 + $22.50 + $94.95$149.35

#51 51. Geometry: A regular octagon

measures (3x + 5) units on each side. What is the perimeter if x = 2?

Each side is 3x + 5 units. 3(2) + 5 = 11

So each side of the octagon is 11 units.How do you find the perimeter of a

shape?Add all the sides.How many sides does an octagon have?(11)(8) = 88 So the perimeter is 88 units.

1-3 HONORS HOMEWORK

P. 19-20 10, 12, 38-46 even, 55, 60 Read 1-4 Take Notes

EXIT SLIP

1. What is the difference between the multiplicative inverse and additive inverse?

2. Does the commutative property always, sometimes or never hold for subtraction? Explain your reasoning.

3. What is the difference between the commutative and reflexive property?

LESSON 1-4 DISTRIBUTIVE PROPERTY

Objectives:By the end of class, students will be able

to: Use the distributive property to evaluate

and simplify expressions.with 90% or above mastery.

P. 25

The Distributive Propertya(b + c) = ab + ac a(b – c) = ab – ac

Example: 4(9 – 7) = 4(9) – 4(7) = 36 – 28 = 8

Example: Julio walks 5 days a week. He walks at a fast rate for 7 minutes and cools down for 2 minutes. Use the distributive property to write and evaluate an expression that determines the total number of minutes Julio walks.

5(7 + 2) 5(7) + 5(2) 35 + 10 = 45 Julio walks 45 minutes total.

11. Time Management: Important FactsIn a week, she uses 5 red, 3 yellow and 4

green dots.How many activities does Margo do in 4

weeks?

4(5 + 3 + 4)4(5) + 4(3) + 4(4) = 20 + 12 + 16 = 48Margo does 48 activities in 4 weeks.

DISTRIBUTIVE PROPERTY AND MULTIPLYING NUMBERS

You can also use the distributive property to multiply numbers easier,

7(49) = 7(50 – 1)

7(50) – 7(1) 350 – 7 = 343

Do p. 29 #3

DISTRIBUTIVE PROPERTY AND MULTIPLYING NUMBERS

14(51) = 14(50 + 1)

14(50) + 14(1) 700 + 14

714So 14(51) = 714

DISTRIBUTIVE PROPERTY AND SIMPLIFYING EXPRESSIONS

You can use the distributive property to simplify expressions. An expression is in simplest form when it has no like terms or parentheses.

Like terms have the same variable and power. See p. 27.

Are 5x3 and 4x2 like terms?

25. 2(x + 4) 2x + 8

Example: -3(3m + 5m) -9m - 15m like terms -24mDo 31 – 39, 43 and 47 odd in your

notebook

27. (4 – 3m)8 4(8) – 2m(8) 32 – 24m

31. 7m + 7 – 5m 2m + 7

33. (2 – 4n)17 2(17) – 4n (17) 34 – 68n

35. 7m + 2m + 5p + 4m13m + 5p

37. 4(fg + 3g) + 5g 4fg + 12g + 5g

4fg + 17g

39. 7 times the sum of a squared and b minus 4 times the sum of a squared and b

7(a2 + b) – 4(a2 + b)7a2 + 7b – 4a2 – 4b

3a2 + 3b

47. 3m + 5g + 6g + 11m11g + 14m

HONORS HOMEWORK

p. 29- 30 26 – 38 even, 42 – 46 even, 50, 56