SAT Readiness. Simplifying Algebraic Expressions 1.4.

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Presentation transcript:

SAT Readiness

Simplifying Algebraic Expressions 1.4

Objectives  Simplify and evaluate algebraic expressions

Why Learn This?  You can model the total point scored in a basketball game by using an algebraic equations  Example f + 2g +3t f = number of 1 point free throws g = number of 2 point shots t = number of 3 point shots

Translating Real-World  Algebraic Expressions ActionOperationPossible Context Clues CombineAddHow many total? Combine Equal Groups MultiplyHow many altogether? SeparateSubtractHow many more? How many remaining? Separate into equal groups DivideHow many in each group?

Words for Operations  + : Add, Combine, Plus, And, Total  - : Subtract, Minus, Less than, Difference,  x : Multiply, Product, Times  ÷ :Quotient, Divide, Divided by

Write an Algebraic Equation to Represent each equation 1) The distance remaining for a runner after m miles of a 26.2 mile marathon m 2) The number of hours it takes to fly 1800 miles at an average rate of n miles per hour. 1800/n

Algebraic Expressions (Cont.) 3) Lucy’s age y years after her 18 th birthday 18+y 4) The number of seconds in h hours. 3600h

PEMDAS 1) Parentheses and grouping symbols 2) Exponents 3) Multiply and Divide from left to right 4) Add and Subtract from left to right

Evaluating Algebraic Expressions Ex) x + 3xy -2y for x = 4 and y=7 = (4) + 3 (4)(7) – 2(7) = – 14 = 74 Ex) b 2 z-2bz+z 2 for b = 6 and z =2 Answer: 52

Combine Like Terms  Simplify the Expressions by adding or subtracting Like terms.  Example: 3x 2 -9xy x 2 -1  Answer: 7x 2 -9xy -1

Like versus Unlike  4xy 2 and -7xy 2 like  2xy 2 and 2x 2 y unlike  1 and -8 like  3x and (1/2)x like  7xy and 4yx like

Simplify the Following Expressions  x 2 + 5x + 2y +7x 2 Answer: 8x 2 + 5x + 2y  b(5a 2 -2a) -11a 2 b+2ab Answer: -6a 2 b

Word Problems a) Holly’s hybrid car gets 45 miles per gallon on the highway and 25 miles per gallon in the city. Write & simplify an expression for the total number of miles she can drive if her fuel tank hold 15 gallons of gas. Let h = # gallons used on the highway. Answer: 45h +25(15-h) = 20h b) How many total miles can she drive on one tank of gas if she used 5 gallons on the highway? Answer: 20(5) = 475

Closure  Simplify the expression: -8x + 10x + 2(3-9x)  Evaluate when x = 2  Homework: Simplifying Expressions & Word Problems Packet