PLEASE BE QUIET after the bell rings! PLEASE HAVE OUT: 1. PENCIL and PAPER (Possibly Eraser and Calculator) 2. Yesterday’s HOMEWORK. PLEASE BE QUIET after the bell rings!

Yesterday’s Homework Assignment -- Tuesday (10/5) Pgs. 29-31: 10, 12, 16, 18, 32. 10. Number of football games and number of years. $530,000 12. Irrelevant: grades student are in. Needed: number of adults.

16. Multiply preceding number by 3; 162, 486, 1,458 Pgs. 29-31: 10, 12, 16, 18, 32. 16. Multiply preceding number by 3; 162, 486, 1,458 18. Subtract 3, then 4, then 5 and so on; 45, 38, 30 32.

Clear-Off-Desk except for: PENCIL and PAPER! Possibly Eraser and Calculator Focus on Lesson!

The operations of addition and multiplication have special properties. 1.7 “The Commutative and Associative Properties” Goal 1 - You will simplify expressions by applying the associative and commutative properties. The operations of addition and multiplication have special properties.

PROPERTIES OF ADDITION AND MULTIPLICATION Commutative Property of Addition In a sum, you can add terms in any order. a + b = b + a 6 + 9 = 9 + 6 Commutative Property of Multiplication In a product, you can multiply factors in any order. ab = ba 6 x 9 = 9 x 6 In Words In Algebra In Arithmetic

PROPERTIES OF ADDITION AND MULTIPLICATION Commutative Property Commute means to change locations. In just addition or just multiplication, changing positions does NOT change the answer.

PROPERTIES OF ADDITION AND MULTIPLICATION Associative Property of Addition Changing the grouping of terms will NOT change the sum. (a + b) + c = a + (b + c) (6 + 9) + 2 = 6 + (9 + 2) Associative Property of Multiplication Changing the grouping of factors will NOT change the product. (ab)c = a(bc) (6 x 9)2 = 6(9 x 2) In Words In Algebra In Arithmetic

PROPERTIES OF ADDITION AND MULTIPLICATION Associative Property Associate means to join or group together. In just addition or just multiplication changing grouping symbols does NOT change the answer.

– Using Commutative Property Example 1 – Using Commutative Property Explain why it does NOT matter which of the two numbers you use as the length when you find the area of a rectangle. 17 ft by 23 ft

– Using Commutative Property Example 1 – Using Commutative Property Solution The area A of a rectangle is the product of its length l and width w. Using the commutative property of multiplication you can write: A = lw = 23 x 17 = 17 x 23. The choice of l does NOT matter. 17 ft by 23 ft

– Using Commutative Property Example 1 – Using Commutative Property However, a  b  b  a 6  2  2  6 While multiplication is commutative (order does NOT matter), division is NOT commutative and order does matter.

– Using Associative Property Example 2 – Using Associative Property Show that: (13 + 8) + 25 = 13 + (8 + 25) Solution Evaluate each expression separately. (13 + 8) + 25 = 21 + 25 = 46 13 + (8 + 25) = 13 + 33 = 46

– Using Associative Property Example 2 – Using Associative Property However, (a – b) – c  a – (b – c) (8 – 5) – 2  8 – (5 – 2) While addition is associative (grouping symbols do NOT matter), subtraction is NOT associative and grouping symbols do matter. (8 – 5) – 2 = 1 8 – (5 – 2) = 5

1.7 “The Commutative and Associative Properties” Are there any questions about The Commutative and Associative Properties of Addition and Multiplication?

Goal 2 - You will justify the process used to simplify expressions. 1.7 “The Commutative and Associative Properties” Goal 2 - You will justify the process used to simplify expressions. Knowing the properties of numbers can help you use mental math to evaluate expressions. When you use a property of numbers to explain why a step of your answer is valid, you are justifying the step.

Example 3 Justifying an Answer Use mental math to evaluate: 43 + (68 + 57). Justify each step. Solution To evaluate 43 + (68 + 57) using mental math, look for numbers that are easy to add first. Notice that the ones’ digits in 43 and 57 are easy to add. So, it is easier to add 43 and 57 than 68 and 57.

Example 3 Justifying an Answer Use mental math to evaluate: 43 + (68 + 57). Justify each step. Solution 43 + (68 + 57) Wrote original problem = 43 + (57 + 68) Commutative Property = (43 + 57) + 68 Associative Property = (100) + 68 Added 43 and 57 = 168 Added 100 and 68

Are there any questions about Justifying Steps? 1.7 “The Commutative and Associative Properties” Are there any questions about Justifying Steps? Classwork 1.7 Pgs. 34 - 35: 1-8 and 26-28

Make sure you have the proper heading and format. 930 Danny Dana 10/1 Math 7 - Dequer 1.7 Pg.34-35: 1-8 & 26-28 1. Please work Quietly and On-Your-Own for 10-15 min. Have out your Dana Planner turned to the Assignment Sheet for Week 5.

Make sure you have the proper heading and format. 930 Danny Dana 10/6 Math 7 - Dequer 1.7 Pg.34-35: 1-8 & 26-28 1. You may now get help from and give help to near neighbors. When your done, check odd numbered problems in the back of the book on SA-2.

1.7 “Guided Practice” Pgs. 34 - 35: 1-8 and 26-28 1. Associative Property - Multiplication 2. Commutative Property - Multiplication 3. Commutative Property – Addition 4. Associative Property – Addition 5. C 6. B 7. D 8. A 26. C 27. J 28. B

Make-Up Tests Math 7 Make-Up Quizzes are available Tomorrow, Thursday (10/7/03), at 7:45 a.m., 12:40 p.m. (during lunch) and/or 3:05 p.m. in Room 29. If it is a retest bring the original Blue Scantron Form and colored quiz (if possible) with you.

Class/Homework Assignment -- Wednesday (10/6) Pgs. 34-35: 10, 12, 14, 18, 22. Work on 1st Quarter Project or Assigned Replacement!