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

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

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

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

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

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

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

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

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

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.

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

On the back of your notes: AdditionSubtraction MultiplicationDivision

Addition Phrases: More than Increase by Greater than AddTotalPlusSum

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

Multiplication Phrases: ProductTimesMultiplyOf Twice or double Triple

Division Phrases: QuotientDivide Divided by Split equally

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

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

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

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

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

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

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 divide g 2.5 divide g