Section 1.3 Algebraic Expressions Sheldon won some money in a biking completion. He has two choices on how he gets paid. Choice #1: $20 per week for one year Choice # 2: $12 per week for one year plus $400 cash now Questions 1.Which method would pay Sheldon more money? Choice 1 choice 2 20x 52= 1040 12x 52 +400 624+400 1024 2.Using Choice #1, how much money would Sheldon have in A) 4 weeks? 20 4 = 80 B) 10 weeks? 20x 10 = 200 3.Describe a rule you can use for Choice #1 to calculate the total money Sheldon receives at any time during the year. 20 x the number of weeks 20x W 4.Using Choice #2, how much money would Sheldon have in A) 12 weeks? 12 x 12 +400 144+400 544 B) 30 weeks? 12x30+400 360+400 760 5.Describe a rule you can use for Choice #2 to calculate the total money Sheldon receives at any time during the year. Multiply the number of weeks by 12 and add on 400........... so 12W + 400 Important Terms Expression: consists of numbers and/or variables which are related by +,-, ⨉, or ÷. It does NOT have an equal sign. Variable: a letter that represents a quantity that can change or vary Numerical Coefficient: the number multiplied by a variable. If there is no number in front of a variable the numerical coefficient is automatically 1. Constant Term: the number in an expression that does not change.... it stays constant. It has no variable attached. 8n + 3 Numerical Coefficient Expression 4x + 7 Constant Variable Numerical Coefficient 4 Variable X Constant 7 3x + 2 3 X 2 7j -1 7 J 1 c+1 1 C 1 m 1 M 8 5 + 3g 8 3 G 5 1 y -2 0 -2 + y Writing Algebraic Expressions Operation Addition Words add the sum of more than increased by the total of plus Subtraction subtract from difference less ( less than) decreased by take away reduced by minus Multiply multiply times the product of multiplied by of double triple Division divide divided by the quotient of the ratio of equal amounts of per Examples Five more than a number → n+5 The sum of a number and ten →n+10 A number increased by 4 →n+4 Seven plus a number →7+n Five less than a number →n-5 A number decreased by six →n-6 A number reduced by eight →n-8 The number subtracted from twenty →20-n The product of a number and four →4n Five times a number →5n A number doubled →2n A number tripled →3n A number divided by two →n/2 A number shared by ten people →n/10 The quotient of a number and three →n/3 Twelve is divided by a number →12/n Write an algebraic expression that has... A). A variable m, a numerical coefficient 4 and a constant term of 7. (4m+7) B). A variable g, a numerical coefficient -3 and no constant term. (-3g) C). A variable y, a numerical coefficient 1 and a constant term of -2. (y-2) Evaluating an Algebraic Expression To evaluate an algebraic expression means to substitute a number for the variable and determine the value of the expression. A). Evaluate 2m 5 if m = 3. 2(3) +5 2 x 3 +5 6+5 11 B). Evaluate 1 d 6 if d = 20. 2 ½ (20)-6 20/2 -6 10-6 4 C). Evaluate 4 x if x = 1. 4-1 3 D). Evaluate 8 m if m = 6. 2 8 – 6/2 8-3 5 Complete Pages 18-19 #’s 1, 2, 4, 5, 7, 8