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

Example 6-1b Vocabulary Equivalent expressions Expressions that have the same value = = = 7

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

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)

Properties PropertyAlgebraArithmetic Commutativea + b = b + a6 + 1 = 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

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

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 ( ) 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 )

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

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

Example 6-2a Use the Distributive Property to write as an equivalent expression. Then evaluate the expression. Write the expression ( ) 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

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

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

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)

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 ( ) 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

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

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

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

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

Example 6-5a Answer: Commutative Property of Addition Name the property shown by the statement 5/7 Write problem = 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

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

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

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

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 

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

End of Lesson 6 Assignment Lesson 1:6Algebra: Properties All