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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?

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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.

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Additive Identity – Any number plus 0 = the number. 0 is called the additive identity. a + 0 = a Example: 2 + 0 = 2 Additive Inverse - Any number and its opposite are additive inverses. Their sum = 0. a + (-a) = 0 Example: 100 + (-100) = 100 - 100 = 0

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Multiplicative Identity – The product of a number and 1 is the number. a 1 = 1 a = a Example:14 1 = 1 14 = 14 Multiplicative Inverse - A number times its reciprocal is 1. a b = 1 b aa, b 0 Example:4 5 = 1 5 4

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Multiplicative Property of 0 – The product of any number and 0 is 0. a 0 = 0 Example:9 0 = 0

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Commutative Property - The order in which you add or multiply doesn’t change their sum or product. a + b = b +a a(b) = b(a) Example: 4 + 8 = 8 + 4 7(11) = 11(7)

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Associative Property – Grouping numbers does not change the sum or product. (a + b) + c = a + (b + c) Example:(3 + 5) + 7 = 3 + (5 + 7)

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Do 37, 39, 43, 45, 47, 57, 58 in your notebook Now lets look at 14.

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14. 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 + 0Multiplicative Property of 0 1Additive Identity

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Properties of Equality Reflexive Property–Any quantity is equal to itself a = a Example: 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.

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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).

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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

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Do p. 31 60, 62

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16. Hotel Rates: Important Facts Mon - Fri $72, Tax $5.40 Sat, 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 = 291 The total cost of the room including tax $291.

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29. Scuba Driving Expression 1: 2($10.95) + 3($7.50) + 2($5.00) + 5(418.99) = $21.90 + $22.50 + $10 + $94.95 $149.35 The 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

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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.

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

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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?

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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.

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The Distributive Property a(b + c) = ab + ac a(b – c) = ab – ac Example: 4(9 – 7) = 4(9) – 4(7) = 36 – 28 = 8

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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.

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11. Time Management: Important Facts In 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 = 48 Margo does 48 activities in 4 weeks.

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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

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14(51) = 14(50 + 1) 14(50) + 14(1) 700 + 14 714 So 14(51) = 714

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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 5x 3 and 4x 2 like terms? 25. 2(x + 4) 2x + 8

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Example: -3(3m + 5m) -9m - 15m like terms -24m Do 31 – 39, 43 and 47 odd in your notebook 27. (4 – 3m)8 4(8) – 2m(8) 32 – 24m

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31. 7m + 7 – 5m 2m + 7 33. (2 – 4n)17 2(17) – 4n (17) 34 – 68n 35. 7m + 2m + 5p + 4m 13m + 5p

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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(a 2 + b) – 4(a 2 + b) 7a 2 + 7b – 4a 2 – 4b 3a 2 + 3b 47. 3m + 5g + 6g + 11m 11g + 14m

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

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