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1. How long does a car traveling at 70 mph take to travel 88 miles, in hours? 1.257 hours 2. How many terms are in the expression: 36x + 27xy – 18y – 9? 3. 4 5 word prediction. Guess the meanings of the following words: Variable, expression, base, constant, & factor. No notes Kilo Hecto Deka BASIC Deci Centi Milli CCCA Unit 1 Why is it important to understand the “language” of mathematics? Identifying Parts Can have variables, numbers, addition, subtraction, multiplication, division, parenthesis, square roots, exponents… Examples: x2 3 x 2 5b 7 c d 5 xy Symbols or letters used to represent an unknown Examples: x How many items are being added, subtracted, divided Examples: 2 5a 2 xy 3 3 P 2x 2 a b 4 Same variable raised to the same power Examples: 2 2 5x y and 8 x y 2 7y and 22y 2 The number in front of a variable Examples: 123 xy 3 2 123 9xy z 9 x 1 The number up in the air next to a base The number of times you multiply something times itself Examples: 3 3 12 12 2 x 4 3 y 7 4 What the exponent sits on The part that has been raised to a power Examples: 3 2 12 x 2 x 4 3 y 7 y A number that has no variable It can be positive or negative Examples: 42 -42 3x 5 5 2 4 5 x 3y 8 -8 Items that are being multiplied together Can be numbers, variables, parenthesis Examples: 6 1 and 6…. Or 2 and 3 9 xy 9 and x and y x 2 y 3 (x + 2) and (y – 3) 3 z 9 3 and (z – 9) Simplify inside parenthesis Take care of exponents In order from left to right, multiplication or division In order from left to right, addition or subtraction Examples: 5 3 2 1 4 2 -18 A variable is a symbol used to represent a number in an expression or an equation. An algebraic expression is a mathematical expression that consists of variables, numbers and operations. Sum Plus Add More Than Increased Difference Minus Decreased Less Than (swaps the order) Quotient Half Divide by Product Twice Double Triple Square Cubed To the power of Raised to a power The sum of a number and 10 x + 10 Fourteen decreased by a number p Seven less than a number t The product of 9 and x squared 2 9x 9 less than g to the fourth power 4 g – 9 8 + 3x Eight increased by three times x 1. 2. 3. The sum of nine and a number x The product of 9 and a number n Thirty-two divided by a number y 1. 2. 3. 4. 5. 6. 7. 8. The difference of 28 and a number One-third the square root of a number Fifteen less than twice a number seven divided by twice a number five more than twice a number three times a number decreased by 11 The product of 5 and the cube of a number increased by the difference of 6 and x Half the sum of x and y decreased by one-third of y Hailey Saunders has $1000 to distribute to her employees as a bonus. How much money will each employee get? Jake’s electric company charges $45 per hour and spends $20 a day on gasoline. Write an algebraic expression to represent his earnings for one day. Olivia makes $100 a day as a math tutor. Write an expression for the amount she makes in d days. WORKSHEET Writing Algebraic Expressions Worksheet Write the following phrases as an algebraic expression. 1. 2. 3. 4. Thirty divided by seven times a number Jenny earns $30 a day working part time at a supermarket. Write an algebraic expression to represent the amount of money she will earn in d days. The product of nine and a number, decreased by six Three times a number, increased by seventeen