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4. Example 6-1b Objective Use addition and multiplication properties to solve problems

5. Example 6-1b Vocabulary Equivalent expressions Expressions that have the same value 4 + 3 = 7 5 + 2 = 7 6 + 1 = 7

6. Example 6-1b Vocabulary Properties Statements that are true for any number or variable

7. Distributive Property PropertyAlgebraArithmetic Distributivea(b + c) = ab + ac4(6 + 2) = 4(6) + 4(2) a(b - c) = ab - ac3(7 - 5) = 3(7) - 3(5) 3 (4 + 6) = 3(4) + 3(6)

8. Properties PropertyAlgebraArithmetic Commutativea + b = b + a6 + 1 = 1 + 6 a · b = b · a7 · 3 = 3 · 7 Associativea + (b + c) = (a + b) + c2 + (3 + 8) = (2 + 3) + 8 a · (b · c) = (a · b) · c3 · (4 · 5) = (3 · 4) · 5 Identitya + 0 = a9 + 0 = 9 a · 1 = a5 · 1 = 5

9. Lesson 6 Contents Example 1Use the Distributive Property Example 2Use the Distributive Property Example 3Use the Distributive Property Example 4Identify Properties Example 5Identify Properties Example 6Identify Properties Example 7Identify Properties

10. Example 6-1a Distribute the 8 to the 5 Use the Distributive Property to write as an equivalent expression. Then evaluate the expression. Write the expression 8 ( 5 + 7 ) Distribute the factor 8 to the numbers inside the parentheses 1/7 8 ( 5 ) Bring down the + 8 ( 5 ) + Distribute the 8 to the 7 8 ( 5 ) + 8 ( 7 )

11. Example 6-1a Multiply first Answer: 96 Use the Distributive Property to write as an equivalent expression. Then evaluate the expression. Follow the order of operations 1/7 Multiply 8(5) Bring down + 8 ( 5 ) + 8 ( 7 ) PEMDAS 40+ Multiply 8(7) 56 Add 40 + 56 96

12. Example 6-1b Answer: 36 Use the Distributive Property to write as an equivalent expression. Then evaluate the expression. 1/7

13. Example 6-2a Use the Distributive Property to write as an equivalent expression. Then evaluate the expression. Write the expression ( 2 + 9 ) 6 2/7 Distribute the factor 6 to the numbers inside the parentheses Distribute the 6 to the 2 Bring down the + (2)6(2)6 +(2)6 + (9)6 Distribute the 6 to the 9

14. Example 6-2a Use the Distributive Property to write as an equivalent expression. Then evaluate the expression. Answer: 66 2/7 (2)6 + (9)6 Follow the order of operations PEMDAS Multiply first Multiply (2)6 12 Bring down + Multiply (9)6 +54 Add 12 + 54 66

15. Example 6-2b Use the Distributive Property to write as an equivalent expression. Then evaluate the expression. Answer: 56 2/7

16. Example 6-3a VACATIONS Mr. Harmon has budgeted $150 per day for his hotel and meals during his vacation. If he plans to spend six days on vacation, how much will he spend? 3/7 Decide how to solve the problem Spend $150 per day 6 days Remember: per refers to multiplication Write expression 6 (150)

17. Example 6-3a VACATIONS Mr. Harmon has budgeted $150 per day for his hotel and meals during his vacation. If he plans to spend six days on vacation, how much will he spend? 3/7 Use the distributive property to solve Decompose 150 6 (150) 6 (100 + 50) Distribute the factor 6 to the numbers inside the parentheses Distribute the 6 to the 100 6(100) 6(100) + 6(50) 6(100) + Bring down the + Distribute the 6 to the 50

18. Example 6-3b Answer: $900 spent on trip 3/7 6(100) + 6(50) Follow the order of operations PEMDAS Multiply first + 600 Bring down + Multiply 6(100) Multiply 6(50) 300 Add 600 + 300 900 Label answer

19. Example 6-3c COOKIES Heidi sold cookies for $2.50 per box for a fundraiser. If she sold 60 boxes of cookies, how much money did she raise? Answer: $150 3/7

20. Example 6-4a Name the property shown by the statement Answer: Identity Property of Multiplication 4/7  Write problem 7 = 1  7 Determine property Multiplying by 1 keeps the same identity of the number Identity Property The process is multiplying Of Multiplication

21. Example 6-4b Answer: Identity Property of Multiplication Name the property shown by the statement. 4/7 

22. Example 6-5a Answer: Commutative Property of Addition Name the property shown by the statement 5/7 Write problem 24 + 5 = 5 + 24 Determine property The numbers have been switched with each other but everything else remains the same Refers to the Commutative Property Commutative Property The process is adding Of Addition

23. Example 6-5b Answer: Commutative Property of Addition Name the property shown by the statement 5/7

24. Example 6-6a Answer: Identity Property of Addition Name the property shown by the statement 6/7 Write problem 7 + 0 = 7 Determine property Adding by 0 keeps the same identity of the number Identity Property The process is adding Of Addition

25. Example 6-6b Answer: Identity Property of Addition Name the property shown by the statement 6/7

26. Example 6-7a Answer: Associative Property of Multiplication Name the property shown by the statement 7/7 Write problem (11  4)  8 = 11  (4  8) Determine property Numbers in same order but have been regrouped with parenthesis Associative Property The process is multiplying Of Multiplication 

27. Example 6-7b Answer: Associative Property of Addition Name the property shown by the statement * 7/7

28. End of Lesson 6 Assignment Lesson 1:6Algebra: Properties11 - 26 All