Variables and Expressions Unit 1 Lesson 2 Variables and Expressions Students will be able to: Write expressions that record operations with numbers and with letters standing for numbers. Key Vocabulary: Variable Constant Expressions Terms Coefficient Variables and Expressions β’ A numerical expression is a mathematical phrase that contains only constants and/or operations β’ To evaluate a numerical expression, you find its numerical value. Variables and Expressions Sample Problem 1: Find the value of each numerical expression. Follow the order of operations when finding each value. a. ππ + ππ ÷ π β π = Variables and Expressions Sample Problem 1: Find the value of each numerical expression. Follow the order of operations when finding each value. a. ππ + ππ ÷ π β π = = ππ + π β π = = ππ β π = = ππ Variables and Expressions Sample Problem 1: Find the value of each numerical expression. Follow the order of operations when finding each value. b. ππ ÷ ππ + π = Variables and Expressions Sample Problem 1: Find the value of each numerical expression. Follow the order of operations when finding each value. b. ππ ÷ ππ + π = =π+π= =π Variables and Expressions Sample Problem 1: Find the value of each numerical expression. Follow the order of operations when finding each value. c. ππ β π β π ÷ π = Variables and Expressions Sample Problem 1: Find the value of each numerical expression. Follow the order of operations when finding each value. c. ππ β π β π ÷ π = = ππ β π = = ππ Variables and Expressions A variable expression is a mathematical phrase that may contain variables, constants, and/or operations. A variable is a letter that is used to represent one or more numbers. The letters π₯ πππ π¦ are used very often as variables in algebra, but variables can be any letter (π§, π, π, π, π ). Variables and Expressions β’ Any number not joined to a variable is called a constant. β’ Itβs called that because its value doesnβt change, even if the value of the variable changes. β’ Each algebraic expression is made up of terms. β’ A term can be a signed number, a variable, or a constant multiplied by a variable or variables. Variables and Expressions β’ Each term in an algebraic expression is separated by a + sign or a β sign. β’ When a term is made up of a constant multiplied by a variable or variables, that constant is called a coefficient. Example: Coefficient ππ + π Variable Constant Variables and Expressions β’ The terms having the same algebraic factors are called like terms. β’ The terms having different algebraic factors are called unlike terms. β’ Expression with one term is called a monomial, with two unlike terms is called a binomial, in general, an expression with one or more than one term (with nonnegative integral exponents of the variables) is called a polynomial. Variables and Expressions Sample Problem 2: Find the terms, constant/s and coefficient/s for each expression. a. ππ β ππ πππ«π¦π¬: πππ«π’πππ₯π: ππ¨π§π¬πππ§π: ππ¨ππππ’ππ’ππ§π Variables and Expressions Sample Problem 2: Find the terms, constant/s and coefficient/s for each expression. a. ππ β ππ πππ«π¦π¬: 2π₯ πππ 10 πππ«π’πππ₯π: π₯ ππ¨π§π¬πππ§π: 10 ππ¨ππππ’ππ’ππ§π: 2 Variables and Expressions Sample Problem 2: Find the terms, constant/s and coefficient/s for each expression. b. π + ππ + ππ πππ«π¦π¬: πππ«π’πππ₯π: ππ¨π§π¬πππ§π: ππ¨ππππ’ππ’ππ§ππ: Variables and Expressions Sample Problem 2: Find the terms, constant/s and coefficient/s for each expression. b. π + ππ + ππ πππ«π¦π¬: π₯ , 4π¦ , πππ 32 πππ«π’πππ₯π: π₯ ,π¦ ππ¨π§π¬πππ§π: 32 ππ¨ππππ’ππ’ππ§ππ: 1 πππ 4 Variables and Expressions β’ Expressions are like instructions that tell you what you have to do to a number or variable. β’ Expressions are used to write word problems in math terms. Variables and Expressions Sample Problem 3: Write an algebraic expression for each verbal phrase. a. A number minus 10 Variables and Expressions Sample Problem 3: Write an algebraic expression for each verbal phrase. a. A number minus 10 π β ππ Variables and Expressions Sample Problem 3: Write an algebraic expression for each verbal phrase. b. The product of a number and 6 Variables and Expressions Sample Problem 3: Write an algebraic expression for each verbal phrase. b. The product of a number and 6 πβπ Variables and Expressions Sample Problem 3: Write an algebraic expression for each verbal phrase. c. 12 less than a number Variables and Expressions Sample Problem 3: Write an algebraic expression for each verbal phrase. c. 12 less than a number π β ππ Variables and Expressions Sample Problem 3: Write an algebraic expression for each verbal phrase. d. 16 plus a number Variables and Expressions Sample Problem 3: Write an algebraic expression for each verbal phrase. d. 16 plus a number ππ + π Variables and Expressions Sample Problem 3: Write an algebraic expression for each verbal phrase. e. The sum of π and 8, divided by 4 Variables and Expressions Sample Problem 3: Write an algebraic expression for each verbal phrase. e. The sum of π and 8, divided by 4 (π + π) ÷ π Variables and Expressions Sample Problem 3: Write an algebraic expression for each verbal phrase. f. 4 more than 2 times a number Variables and Expressions Sample Problem 3: Write an algebraic expression for each verbal phrase. f. 4 more than 2 times a number π + ππ Variables and Expressions Substituting Values into Algebraic Expressions To evaluate an algebraic expression, you substitute values for the variables and then simplify the resulting numerical expression. Variables and Expressions Sample Problem 4: Evaluate each expression using the values given. a. π+π ππππ π = π πππ π = π Variables and Expressions Sample Problem 4: Evaluate each expression using the values given. a. π+π= =π+π= =π ππππ π = π πππ π = π Variables and Expressions Sample Problem 4: Evaluate each expression using the values given. b. ππ β π ππππ π = π πππ π = π Variables and Expressions Sample Problem 4: Evaluate each expression using the values given. b. ππ β ππ ππππ π = π πππ π = π =πβπβπβπ= = ππ β π = = ππ Variables and Expressions Sample Problem 4: Evaluate each expression using the values given. c. πππ β π π + π ππππ π = π πππ π = π Variables and Expressions Sample Problem 4: Evaluate each expression using the values given. c. πππ β π π + π ππππ π = π πππ π = π = ππ β π β π π + π = = ππ β π β π = = ππ β ππ = = ππ Variables and Expressions Sample Problem 5: If π = π, π = π, and π = π, evaluate the following by substituting these values into the following expressions. a. π + ππ ÷ π = Variables and Expressions Sample Problem 5: If π = π, π = π, and π = π, evaluate the following by substituting these values into the following expressions. a. π + ππ ÷ π = =π+πβπ÷π= = π + ππ ÷ π = =π+π= = ππ Variables and Expressions Sample Problem 5: If π = π, π = π, and π = π, evaluate the following by substituting these values into the following expressions. b. ππ + πππ β π = Variables and Expressions Sample Problem 5: If π = π, π = π, and π = π, evaluate the following by substituting these values into the following expressions. b. ππ + πππ β π = =πβπ+πβπβπβπ= = ππ + ππ β π = = ππ + ππ = = ππ Variables and Expressions Sample Problem 5: If π = π, π = π, and π = π, evaluate the following by substituting these values into the following expressions. c. ππ + ππ = π Variables and Expressions Sample Problem 5: If π = π, π = π, and π = π, evaluate the following by substituting these values into the following expressions. c. ππ + ππ = π πβπ+πβπ = = π ππ + π ππ = = =π π π
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