Section 3.1 Variables, Expressions and Order of Operations

Transcription

1 Section.1 Variables, Expressions and Order of Operations A variable is a symbol, usually a letter of the alphabet that represents some varying or undetermined number. An algebraic expression is a mathematical expression or statement, which involves variables, numbers, and operation symbols. (This is NOT an equation.) Example 1: Write an algebraic expression that corresponds to each statement. State clearly what each variable represents. a. Twice the width of a room plus 6 feet. B. Three years less than half of Bob s age. c. The number of wheels in a garage filled with bicycles and tricycles. d. Apples cost $1.19 per pound and bananas cost $0.49 per pound. Describe the cost of buying apples and bananas in terms of the number of pounds of each fruit purchased. e. The amount of money in a jar filled with nickels and pennies. Section.1 Variables, Expressions and Order of Operations 1

2 Order of Operations The order in which arithmetic operations are performed is summarized below: Parenthesis Exponents Multiply Divide Add Subtract PEMDAS When multiplying and dividing, do this from left to right. Same when adding and subtracting. Example 2: Evaluate each of the following. a. 2 2 ( ) b (5 2) c. ( ) ( ) Section.1 Variables, Expressions and Order of Operations 2

3 Using the Order of Operations Rule We can use the order of operations rule to evaluate expressions that are given in variables with appropriate values for the variables stated. Example : Evaluate 2 2x xy + 5y if x = -2 and y = -. 2( ab bc) + a Example 4: Evaluate 2 2 b c if a = 5, b = and c = -1. Section.1 Variables, Expressions and Order of Operations

4 Example 5: A national cable company offers a promotion for its monthly digital cable television service for $49.95 per month. This includes two pay-per-view movies. Additional pay-per-view movies cost $4.95 each. What will be the pre-tax bill if you watch a total of 15 pay-per-view movies this month? a. Define a variable and write an expression that describes the situation. b. Use the expression in part a to answer the question. Example 6: If the sales tax on an item is 8.25%, write an expression that describes the total amount paid on the item. What will be the total amount paid on an item that costs $22.61? Section.1 Variables, Expressions and Order of Operations 4

5 Popper Simplify ( ) A. 11/10 B. 11/20 C. 1/10 D. None of the above (5 2) 4 +8*2 A. -2 B. 2 C. 1/2 D. None of the above. ( ) ( ) (7*4) A. 0 B. -48 C. 48 D. None of the above 2( ab bc) + a 4 Evaluate 2 2 b c if a = 1, b = -1 and c =. A. 1/10 B. - 1/2 C. 1/2 D. None of the above 5 Evaluate 2 2x xy + 5y if x = -20 and y = 0. A. 800 B C. 248 D. None of the above Section.1 Variables, Expressions and Order of Operations 5

6 6 : If the sales tax on an item is 8.25%, write an expression that describes the total amount paid on the item.x A. x (x) B (x) C. x+82.5(x) D. None of the above 7 For problem 6 find the cost of an item that cost 20 dollars A. $1.65 B. $21.65 C. $2.48 D. None of the above For the following, choose the correct expression. 8 Half the width of a room plus 9 feet. A. width+9 B. 0.9width+ 0.5 C. 0.5width+9 D. None of the above 9. Three years more than twice of Bob s age. A.. 2+(Bob age) B. +2(Bob age) C. -2(Bob age) D. None of the above 10 Oranges cost $2 a dozen and bananas cost $0.49 per pound. Describe the cost of buying two dozen oranges and one-pound bananas. A.. $4.49 B.$.49 C. $24.49 D. None of the above Section.1 Variables, Expressions and Order of Operations 6