Copy of Algebraic expressions Study Guide for Math 7.docx



Name__________________________________________________________ Period ________Math 7 Chapter 5Study GuidePART 1: Order of OperationsComplete the following information about the order of operations:What does “PEMDAS” or “Please Excuse My Dear Aunt Sally” mean? Please tell what each letter/word stands for.Parentheses Exponents Multiply and Divide Add and SubtractWhat is special about the order in which you add and subtract and multiply and divide? You do them in order from left to rightPART 2: Evaluating Algebraic ExpressionsEvaluate each expression if r = 5, s = 2, t = 7, and u = 1. Show all work, and all steps. You must rewrite the problem and each step along the way.10 – s + t4) 2r – 4 10-2+72?5-4 8+7 10-4 15 6 13 – s + 10 6) 42 - 2?3 + (2 + r) t 13 -2+1042 - 2?3 + (2 + 5) 742 - 2?3 + 7 16 - 6 + 7 11+10 10 + 7 7 17 21 = 7 3PART 3: Writing Algebraic ExpressionsWrite an algebraic expression for each situation and use it to solve the given situation.? 7.) For Luke to have a birthday party at Sky Zone it cost $100 plus 7.) _f=number of friends__ $9 per friend. Write an algebraic expression that represents (define the variable) the cost of inviting any number of friends. Then use it to find? _____9f+100________ the cost of inviting 9 friends to his party. (algebraic expression) ? ____$181_________ (solution) ? You are going to the store to buy chips and pop. The pop is? 8.)_p=pop bottles_c= chips_ $1.50 per bottle and the chips cost $2.00 for each bag. Write? (define the variable) an algebraic expression to represent the total cost of buying? any number of chips and any number of pop bottles.? _____1.50p+2.00c_____ Use it to find the cost of buying 6 bags of chips and 4 bottles (algebraic expression) of pop. 1.50 ? 4 + 2.00 ? 6 6.00 + 12.00 $18.00 ___$18.00________ (solution) The cost of tickets to the movies is $7 per student. Write and 9.) _s=number of students_ algebraic expression that can be used to find the cost of any (define the variable) number of students. Use your expression to find the cost of 20 students. ___7s_____________ 7?20=140 (algebraic expression) ___$140_________ (solution)PART 4: Identifying PropertiesA. Name the property illustrated in each example.10.) 2 + 3 = 3 + 2 11.) a + 0 = aCommutative Property of AdditionAdditive Identity12.) (12?2)?4=12?(2 ?4)13.) a ? b = b ? aAssociative Property of MultiplicationCommutative Property of Multiplication14.) 6 ? 1 = 615.) a + b = b + aMultiplicative IdentityCommutative Property of Addition16.) (a+b)+c = a+(b+c)17.) 3(2 + 4) = 3 ? 2 + 3 ? 4Associative Property of AdditionDistributive PropertyB. Rewrite each expression to illustrate the given property.17.) Rewrite to illustrate the associative property of addition 2 + (12 + 4) = (2 + 12) + 418.) Rewrite to illustrate the commutative property of multiplication 6 ? a = a ? 6 19.)Rewrite to illustrate the associative property of multiplication (12 ? 4) ? a = 12 ? (4 ? a)20.)Rewrite to illustrate the commutative property of addition? 2x + 3 = 3 + 2xC. Answer each question and provide an example 21.) Does the commutative property apply to division? If false, provide a counterexample to illustrate. If true provide an example to illustrate. False 15 divided by 3 = 5 but 3 divided by 15= 1/522.) Does the associative property apply to subtraction? If false, provide a counterexample to illustrate. If true provide an example to illustrate. False (5-2)-1=2 but 5-(2-1)=4PART 5: Simplifying Algebraic ExpressionsA. Answer the following questions about algebraic expressions. ?23.) Like terms are terms that have the same ___variable______________.24.) If a term has no co-efficient such as x, the “invisible” co-efficient is a ___1_____.25.) We can only add or subtract terms that are __like____ terms.B. Simplify.25.) 5x + 7x 27.) 2y + 4y + 9 12x6y + 928.) 9x + 4y – 4x + 5y + 2 29.) 10x + 4y + 3 – 2x + 3y + 4 5x + 9y + 28x + 7y + 7PART 6: Distributive PropertyUse the Distributive Property to rewrite each expression.30.)2(5 + 3)31.) 6(a - 6)32.) 2(2x + 5) 2 ? 5 + 2 ? 36 ? a - 6 ? 62 ? 2x + 2 ? 5 10 + 6 6a - 36 4x + 10 16Simplify the following algebraic expressions. Use the Distributive Property when appropriate.33.)3(g + 9) + 6g34.)x + 3(7x - 2)35.)6(y - 2) + 12 3 ? g + 3 ? 9 + 6gx + 2 ? 7x + 3 ? -26 ? y + 6 ? -2 + 12 3g + 27 + 6gx + 14x + - 66y + -12 + 12 9g +2715x + -6 0r 15x-66yPART 7: Factoring Linear ExpressionsFind the GCF (greatest common factor) of each pair of monomials.36.)12, 1837.)8xy, 16y38.)12x, 21xy 6 8y 3xFactor each expression. If the expression cannot be factored, write cannot be factored.39.) 35x + 1540.)20 - 16y41.) 14p + 20 5 is factor of both terms4 is factor of both terms2 is factor of both terms 35x divided by 5 is 5x20 divided by 4 is 514p divided by 2 is 7p15 divided by 5 is 3 so,16y divided by 4 is 4y so,20 divided by 2 is 10 so, 5(7x+3)4(5-4y)2(7p + 10)42.)23q - 1043.)12 + 15h44.)3x + 163 is factor of both terms no common factors 12 divided by 3 is 4 no common factors15h divided by 5 is 3h so,3(4 + 3h) 45)12x + 9x 3x is a factor of both terms12x divided by 3x is 49x divided by 3x is 3 so, 3x(4 + 3) ................
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