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Writing Algebraic Expressions Objectives: know algebra termsknow algebra terms write an algebraic expression for a word phrasewrite an algebraic expression for a word phrase write a word phrase for an expression write a word phrase for an expression

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Definitions Variable – A variable is a letter or symbol that represents a number (unknown quantity). 8 + n= 12

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Definitions A variable can use any letter of the alphabet. n+ 5 x– 7 w- 25

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Definitions Algebraic expression – a group of numbers, symbols, and variables that express an operation or a series of operations. m + 8 r – 3

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Definitions Algebraic equation – an algebraic form containing an = sign g + 6 = 45 76 – t = 50

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Definitions Terms – are algebraic forms separated by + and – signs, the signs being included 3x + 2y - 9 -6t - 4s + 5f - 2

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Definitions Like terms – are terms with exactly the same variable form 7x, 5x, 6x, -12x, -6x -t, 3t, -8t, 9t 4r, 6y, -9r, 2y, -y, s, 18y, 4s, -9

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Definitions Constant term / constant – term which does not contain a variable 2x + 4y -9 4h + 2 3e – 2t

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Definitions coefficient – numerical part of a term including its sign 5w - 9 7y – 3z – h -5r + 2s - 8

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Although they are closely related, a Great Dane weighs about 40 times as much as a Chihuahua. When solving real-world problems, you will need to translate words, or verbal expressions, into algebraic expressions. An expression for the weight of the Great Dane could be 40c, where c is the weight of the Chihuahua.

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Notes In order to translate a word phrase into an algebraic expression, we must first know some key word phrases for the basic operations.

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On the back of your notes: AdditionSubtraction MultiplicationDivision

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Addition Phrases: More than Increase by Greater than AddTotalPlusSum

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Subtraction Phrases: Decreased by Difference between Take Away LessSubtract Less than* Subtract from*

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Multiplication Phrases: ProductTimesMultiplyOf Twice or double Triple

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Division Phrases: QuotientDivide Divided by Split equally

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Notes Multiplication expressions should be written in side-by-side form, with the number always in front of the variable. 3a 2t 1.5c 0.4f

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Notes Division expressions should be written using the fraction bar instead of the traditional division sign.

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Write Algebraic Expressions for These Word Phrases Ten more than a number A number decrease by 5 6 less than a number A number increased by 8 The sum of a number & 9 4 more than a number n + 10 w - 5 x - 6 n + 8 n + 9 y + 4

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Examples Addition phrases: 3 more than x 3 more than x the sum of 10 and a number c the sum of 10 and a number c a number n increased by 4.5 a number n increased by 4.5

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Examples Subtraction phrases: a number t decreased by 4 the difference between 10 and a number y 6 less than a number z

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Examples Multiplication phrases: the product of 3 and a number t the product of 3 and a number t twice the number x twice the number x 4.2 times a number e 4.2 times a number e

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Examples Division phrases: the quotient of 25 and a number b the quotient of 25 and a number b the number y divided by 2 the number y divided by 2 2.5 divide g 2.5 divide g

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AF 1.1 Write equations using variables. Definitions Variable – A variable is a letter or symbol that represents a number (unknown quantity). 8 + n = 12.

AF 1.1 Write equations using variables. Definitions Variable – A variable is a letter or symbol that represents a number (unknown quantity). 8 + n = 12.

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