Presentation on theme: "Columbus State Community College"— Presentation transcript:
1 Columbus State Community College Chapter 2 Section 1Introduction to Variables
2 Introduction to Variables Identify variables, constants, and expressions.Evaluate variable expressions for given replacement values.Write properties of operations using variables.Use exponents with variables.
3 Expressions, Variables, and Constants EXAMPLE Writing an Expression and Identifying the Variable and ConstantWrite an expression for each rule. Identify the variable and the constant.(a) Maria increased her test average by 12 points.VariableaConstant(b) The price of a game dropped by $20Variablep – 20Constant
4 Evaluating an Expression EXAMPLE Evaluating an ExpressionUse this rule for finding the price of a game: The price of a game dropped by $20. The expression is p – 20.(a) Evaluate the expression when the original price is $90.p – 20Replace p with 90.90 – 20Follow the rule. Subtract to find 90 – 20.70The new price will be $70.
5 Evaluating an Expression EXAMPLE Evaluating an ExpressionUse this rule for finding the price of a game: The price of a game dropped by $20. The expression is p – 20.(b) Evaluate the expression when the original price is $78.p – 20Replace p with 78.78 – 20Follow the rule. Subtract to find 78 – 20.58The new price will be $58.
6 Numerical Coefficients The number part in a multiplication expression is called the numerical coefficient, or just the coefficient.3x –4m –d n3x –4m –1d nThe numerical coefficients are 3, –4, –1, and 1 respectively.
7 CAUTIONCAUTIONIf an expression involves adding, subtracting, or dividing, then you do have to write +, –, or ÷. It is only multiplication that is understood without writing an operation symbol.5 + x – x ÷ x xAdd xSubtract xDivide by xMultiply by x
8 The Perimeter of a “STOP” Sign The shape of a common “STOP” sign is called an “Octagon.” An octagon has 8 equal sides as shown in the diagram below.To find the distance around an object, called the perimeter, simply add the outside edges together. The expression (rule) can be written in shorthand form as shown below.sssSTOPss8 ssss
9 Evaluating an Expression with Multiplication EXAMPLE Evaluating an Expression with MultiplicationThe expression (rule) for finding the perimeter of an octagon is 8s. Evaluate the expression when the length of one side of the “STOP” sign is 15 inches. See the diagram below.15 in.8 sReplace s with 15 inches.15 in.15 in.STOP8 • 15 inchesMultiply.15 in.15 in.120 inches15 in.15 in.The total distance around this “STOP” sign (perimeter) is 120 inches.15 in.
10 Evaluating an Expression with Several Steps EXAMPLE Evaluating an Expression with Several StepsA car rental company charges a flat fee of $50 plus $30 per day to rent a certain car. The expression (rule) for finding the amount to charge a customer is shown below. Evaluate the given expression for a person who rents this car for 6 days.30dReplace d with 6, the number of days.30 ( 6 )Follow the order of operations. Multiply first.Add.230The cost of renting the car for 6 days is $230.
11 A Rectangular GardenSuppose you wanted to put a fence around a rectangular-shaped flower garden. The length of the garden is 24 feet and the width is 16 feet. How much fencing material would you need to finish the job?24 feet16 feet16 feet24 feet24 feet+ 16 feet+ 24 feet+ 16 feet= 80 feet of fencing
12 RectanglesIn general, the expression (rule) for finding the amount of fencing needed to surround a rectangular garden can be found as follows.lwwll+ w+ l+ w= 2l + 2w= amount of fencing
13 Evaluating an Expression with Two Variables EXAMPLE Evaluating an Expression with Two Variables(a)The expression (rule) for finding the perimeter of a rectangle is 2l + 2w. Evaluate the expression of a rectangular table that has a length, l, of 5 feet and a width, w, of 2 feet.2 l wReplace l with 5 feet and w with 2 feet.2 ( 5 feet ) ( 2 feet )There is no operation between the 2 and the l and there is no operation between the 2 and the w, so it is understood to be multiplication.10 feet feetAdd.14 feetThe perimeter of this table is 14 feet.
14 Evaluating an Expression with Two Variables EXAMPLE Evaluating an Expression with Two Variables(b)Complete the table below to show how to evaluate each expression.Expression ( Rule )Value of aValue of ba – ba • b1.575 – 7 is –25 • 7 is 352.–49–4 – 9 is –13–4 • 9 is –363.6–36 – –3 is 96 • –3 is –184.–2–8–2 – –8 is 6–2 • –8 is 16
15 Writing Properties of Operations Using Variables EXAMPLE Writing Properties of Operations Using VariablesUse the variable n to state this property: When any number is divided by 1, the quotient is the number.Use the letter n to represent any number.n1=
16 Understanding Exponents Used with Variables EXAMPLE Understanding Exponents Used with VariablesRewrite each expression without exponents.(a) m5can be written as m • m • m • m • mm is used as a factor 5 times.(b) 8 x y4can be written as • x • y • y • y • yCoefficient is 8.y4(c) –5 b3 c2can be written as –5 • b • b • b • c • cThe exponent applies only to y.Coefficient is –5.b3c2
17 Evaluating Expressions with Exponents EXAMPLE Evaluating Expressions with ExponentsEvaluate each expression.(a) g2 when g is –4g means g • gReplace each g with –4.–4•–4Multiply –4 times –4.16So g2 becomes ( –4 )2, which is ( –4 ) ( –4 ), or 16.
18 Evaluating Expressions with Exponents EXAMPLE Evaluating Expressions with ExponentsEvaluate each expression.Replace m with –3, and replace n with –2.Multiply two factors at a time.(b) m3 n2 when m is –3 and n is –2So m3 n2 becomes ( –3 )3 ( –2 )2, which is( –3 ) ( –3 ) ( –3 ) ( –2 ) ( –2 ), or –108.m3 n2 means m • m • m • n • n–3•–2• –3 • –2 • –2– • –2 • –2• –2–108
19 Evaluating Expressions with Exponents EXAMPLE Evaluating Expressions with ExponentsEvaluate each expression.Replace w with –4 and replace v with 3.Multiply two factors at a time.(c) –2 w v2 when w is –4 and v is 3So –2 w v2 becomes –2 ( –4 ) ( 3 )2, which is( –2 ) ( –4 ) ( 3 ) (3 ), or 72.–2 w v2 means –2 • w • v • v–2•–43• • 3• 372
20 Introduction to Variables Chapter 2 Section 1 – CompletedWritten by John T. Wallace