The document discusses various mathematical properties including: - Commutative and associative properties of addition and multiplication which allow changing the order or grouping of terms. - Identity properties which show that adding or multiplying a number by its identity (0 for addition, 1 for multiplication) does not change the number. - The opposite property which involves changing all addition signs to subtraction or multiplying the entire expression by -1. - The distributive property which allows multiplying a number by the terms inside parentheses. - Properties of equality including reflexive, symmetric, transitive, and substitution properties which define when expressions can be said to be equal.

1. Math Laws Properties of Addition, Multiplication, and Equalities

2. Warm-Up

3. Warm-Up

4. What’s the Deal? In these lessons we will use the commutative, associative, and distributive properties of addition and multiplication. We will use the reflexive, symmetric, transitive, and substitution properties of equality. We will be reminded of the additive inverse and identity properties.

5. Properties of Addition and Multiplication Commutative Associative Examples: 4+3=3+4 71*25 = 25*71 (6+7)+9=6+(7+9) (8*10)*73=8*(10*73)

6. Nicknames Commutative Property Associative Property Order Property Grouping Property

7. Complete each step and name the property used 24+(27+56) = (27 +__) + 56 = 27 + (24 + __ ) = 27 + __ = ____ Given Commutative Property Associative Property Addition

8. Identity Properties 208 = 208 What number can we add to 208 to get the same answer? (208) 208+0 = 208 Identity Property of Addition 98 = 98 What number can we multiply by 98 to get the same answer? (98) 98*1 = 98 Identity Property of Multiplication

9. What is the opposite? 15x – 8y + 7 Two Ways: Change all signs or, Multiply all terms by -1 One way: -1(15x-8y+7) = -15x + 8y – 7 OR +15x – 8y +7 -15x +8y -7

10. I MUST GET PAID! Nora has two part-time jobs. She gets paid $8 per hour at the retail store and $12 per hour typing term papers for college students. How much will she be able to deposit into her piggy bank after working 7 hours at the store and 5 hours of typing? (8*7)+(5*12) $56+$60=$106

11. Copyright D DAHLBERG Woodard Bay WIldlife Sanctuary Olympia, Washington

12. Pg. 86: 12; 15-21; 43, 44 Assignment

13. Distributive Property & Properties of Equality

14. Transitive Property of Equality a = a Looks pretty straightforward.

15. Symmetric Property of Equality If b = a, then a = b If n = 99, then 99 = ____.

16. Transitive Property of Equality If a = b, and a=c, then a = c If x = 42, and n=(42), then x = ____. Hint: any time you see trans- in part of a word, the meaning usually involves “across”.

17. Substitution Property of Equality If b = a, then a = b If x = (44-2), and n=(40+2), then x = __. 42

18. Distributive Property of Multiplication 35(20 + 9) means 35 x everything in the parentheses. 35*20 + 35 *9 = 700 + 315 =1015 755 * 45 = (700 + 50 + 5)•45 (700•45)+ (50•45)+ (5•45)

19. Try Some 9 (5+y)= 45 + 9y 14(x-5)= 14x - 70 3(n+2)= 3n + 6 3p(r+2)= 3pr+3p2

20. Write these using the Distributive Property rs+rq 4bk + sk 9xy – 21xyz 10fg – 2kg Start by finding the factors that are common to both terms. The first one shows r is common to both. r(s+q) k(4b + s) 3xy(3 – 7z) 2g(5f – 2k)

21. assignment Pg 86: 24-31; 33-37; 45, 47 all