1-3: Algebraic Expressions

Transcription

1 1-3: Algebraic Expressions Mr. Gallo Algebra Modeling Words with an Algebraic Expression What algebraic expression models the word phrase seven fewer than a number t? t 7 What algebraic expression models the word phrase two times the sum of a and b? a b Identify the actions that suggest operations Define one or more variables to represent the unknown(s). Represent the actions using the variables and the operations. 1

2 Modeling a Situation You are on a bicycle trip. You traveled 5 miles the first day. Since then, your average rate has been 1 miles per hour. What algebraic expression models the distance you traveled so far? Relate Miles traveled the first day plus Amount traveled per hour times Number of hours since day 1 Define Let h =the number of hours Write 5 1 h The expression 5 1h models this situation. Evaluating Algebraic Expressions Evaluate Substitute a number for each variable in the expression Simplifying using the Order of Operations (PEMDAS) What is the value of the expression for the given values of the variables? r5 s6 1 for r 3 and s9 3 d 1 c - for c and d

3 Writing and Evaluating an Expression Ticket prices for admission to a museum are $8 for adults, $5 for children and $6 for seniors. a. What algebraic expression models the total number of dollars collected in ticket sales? b. If 0 adult tickets, 16 children s tickets and 10 senior tickets are sold one morning, how much money is collected in all? a. Let a = # of adult tickets c = # of children s tickets 8a 5c 6s T b Let s = # of senior tickets T = total money collected 610 T T 300 T There was $300 collected in all from ticket sales. Vocabulary Term An expression that is a number, a variable or the product of a number and one or more variables. 100 z 35x yz Constant term A term with no variables 100 Like Terms Have the same variables raised to the same powers 35x yz 6x yz 35x yz 4x 6x yz 4y 6 Like Terms Terms Constant Term 3

4 Properties for Simplifying Algebraic Expressions Let a, b and c represent real numbers: Definition of Subtraction a bab Definition of Division aba 1, b0 Distributive Property for Subtraction Multiplication by 0 Multiplication by -1 Opposite of a Sum Opposite of a Difference Opposite of a Product Opposite of an Opposite b a b c abac 0a 0 1aa ab ab ab ab abba ab ab ab a a Simplifying Algebraic Expressions Combine like terms. What is a simpler form of each expression? x 4y 53x y a 3b 6b 5a 7a 9b x 4y15x5y 14x 9y Complete the Got It? #5 on p. 1 a. 3j 7k 5j b. 1a 53b 4

5 1-4: Solving Equations Mr. Gallo Algebra Review of Properties Properties of Equality Assume a, b and c represent real numbers. Property Definition Example Reflexive Symmetric Transitive Substitution a a If a b, then b a If ab and bc, then ac If a b, then you can replacd a with b and vice versa If.5, then.5 If.5 1 and 1 5, then.5 5 If a b and 9 a 15, then 9b 15 5

6 Review of Properties cont. Properties of Equality Assume a, b and c represent real numbers. Property Definition Example Addition If ab, then acbc If x1, then x3 1 3 Subtraction If ab, then acbc If x1, then x3 1 3 Multiplication Division If a b, then ac bc If ab, then acbc with c 0 If x1, then x3 13 If x1, then x3 1 3 Solving equations with more than one operation (variables on both sides) 1) Simplify both sides of the equation by combining like terms. ) Collect all variables to one side and constants to the other side. (Addition or Subtraction Property of Equality) 3) Simplify both sides of the equation by combining like terms again. 4) Multiply or divide to make the coefficient of the variable equal 1. (Multiplication or Division Property of Equality) 5) Check your answer by substituting the result back into the original equation. 6

7 Example : Solve the following equation y1 16 y y16 y y 18 y y y 3y y 6 Distributive Property Subtraction Property of Equality Division Property of Equality Subtraction Property of Equality Check: Ex. 5: If $1000 is in a bank account earning 5% simple interest, the dollar value of the account A in t years is given by A t. What is t in terms of A? A t A t A t A 0 t 50 7

8 Homework: p #11, 0-4, 8, 30, 3, 33, odd, 46, 59, 6, even 8