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Section 1-1: Using Variables Objectives: (1) To model relationships with variables (2) To model relationships with equations Definitions • A variable is a symbol, usually a letter, that represents one or more numbers. • An algebraic expression is a mathematical phrase that can include numbers, variables and operational symbols. • An equation is a mathematical statement that says two or more expressions are equal. Applying Words to Symbols • Addition – Sum • Ex: The sum of a 12 and a number • 12 + x – More than • Ex: 3 more than a number • x+3 – Plus • Ex: a number plus 6 • n+6 Applying Words to Symbols (Cont’) • Subtraction – Difference • Ex: The difference of a number and 8 • x–8 – Less than • Ex: A number less than 7 • 7–x – Decreased by • Ex: 10 decreased by a number. • 10 – y – Subtracted From • 5 subtracted from a number • x–5 Applying Words to Symbols (Cont’) • Multiplication – Times • Ex: A number times 5 • x5 – Multiplied By • Ex: 2 multiplied by a number • 2x – Product • Ex: the product of a number and 4 • x4 – Of • Ex: one-fifth of a number • 1/5 x Applying Words to Symbols (Cont’) • Division – Quotient • Ex: The quotient of 3 and a number • 3/x or 3 ÷ x – Divided by • Ex: A number divided by 9 • x/9 or x ÷ 9 What Out for Combos!!! • Ex: The sum of 3 times a number and 7 3x + 7 • Ex: Twice a number divided by 3 2x/3 • Ex: 1/8 of a number 1/8 x • Ex: 4 times the sum of a number and 2 4 (x + 2) Writing Expressions to Represent a Data Table Suppose you had a job that paid $8 an hour. How much money would you make in an hour? If you said $8, you’d be correct. How much would you make in 3 hours? 7 hours? If you said, “$24 and $56” you be correct again. Pat yourself on the back! Writing Expressions to Represent a Data Table Hours Worked Money Earned 1 18=8 2 2 8 = 16 3 3 8 = 24 7 7 8 = 56 h 8 h = 8h This is the expression we are looking for! Writing Expressions to Represent a Data Table • Find the pattern • Express the pattern mathematically – Hence the term expression • Then you’re done!