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Variable Expressions 2009 SOL A.1 Varina High School Tammy Wallace Vocabulary • A variable is a symbol, usually a letter, used to represent a quantity. This quantity represents an element of any subset of the real numbers. • An algebraic expression may contain numbers, variables, operations, and grouping symbols. An algebraic expression may be evaluated by substituting values for the variables in the expression. How are algebraic expressions used in Algebra? • Algebraic expressions can be translated to verbal expressions or word phrases • Verbal expressions or word phrases, which describe characteristics of given conditions, can also be translated into algebraic expressions for the purpose of evaluation. In expressions, there are many different ways to write multiplication: 1. 𝑎𝑏 2. 𝑎 ∙ 𝑏 3. 𝑎 𝑏 or 𝑎 𝑏 4. (𝑎)(𝑏) 5. 𝑎 x 𝑏 We are not going to use the multiplication symbol (#5) any more. Why do you think we will not use this anymore? Division, on the other hand, is written as: 1) 𝑥 3 2) 𝑥 ÷ 3 Here are some phrases you may have listed. The terms with * are ones that are often used. Addition Subtraction Multiplication Division Exponents sum difference produce quotient power of ___ increase decrease times divided squared plus minus multiplied ratio cubed add subtract more than less than total Writing Algebraic Expressions Steps for Writing Algebraic Expressions: 1. Read for understanding 2. Define the variable 3. Translate the words into numbers/variables/operations 4. Write as an expression Define a variable and write an algebraic expression for each phrase. two times a number plus 5 Read for understanding two times a number plus 5 Define the variable. This can be whatever you want it to be Let x = “a number” Translate to numbers two times 2∙ a number plus 5 𝑥 +5 Write as an expression 𝟐𝒙 + 𝟓 7 less than three times a number (NOTE: when the words “more than” or “less than” are used, write the expression opposite than how you read it) Read for understanding 7 less than 3 times a number Define the variable Let x = “a number” Translate to numbers 7 less than 𝑠𝑜𝑚𝑒𝑡ℎ𝑖𝑛𝑔 − 7 3 times a number 3∙ 𝑥 Write as an expression 𝟑𝒙 − 𝟕 The absolute value of the sum of a number a 5 Read for understanding the absolute value of the sum of a number and 5 Define the variable Let x = “a number” Translate to numbers the absolute value of ? the sum of ? +? Write as an expression 𝒙+𝟓 a number and 5 𝑥 and 5 The quotient of a number cubed and 12. Read for understanding quotient of a number cubed and 12 Define the variable Let x = “a number” Translate to numbers quotient of ? ? a number cubed and 12 𝑥 ?3 𝑎𝑛𝑑 12 Write as an expression 𝒙𝟑 𝟏𝟐 The square root of the product of 6 and a number squared. Read for understanding the product of square root of Define the variable 6 and a number squared Let x = “a number” Translate to numbers square root of ? the product of 6 and a number squared ?∙? 6 and 𝑥 2 Write as an expression 𝟔𝒙𝟐 Write an verbal expression for each algebraic expression 𝟖+𝒂 Answers may vary Write an verbal expression for each algebraic expression 𝒎 𝟒 Answers may vary Write an verbal expression for each algebraic expression 𝟑 𝒏−𝟓 Answers may vary Write an verbal expression for each algebraic expression 𝒙𝟐 + 𝟔 Answers may vary