SAT Readiness

25 (E) 2 (D) 1 (C) 1- (B) 2- (A)x? of value the is what -2, yand y-3x If 2

100.00 (E) 20.00 (D) 6.25 (C) 3.16 (B) 2.50 (A)

?21

k when x of value the is what

,k5

yand yx If 2

5 (E) 2 (D) 0 (C) 4- (B) 6- (A)minimum? its at 2)-(x6f(x) is x of value what For 2

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 throwsg = number of 2 point shotst = number of 3 point shots

Translating Real-World Algebraic Expressions

Action Operation Possible Context Clues

Combine Add How many total?

Combine Equal Groups

Multiply How many altogether?

Separate Subtract How many more? How many remaining?

Separate into equal groups

Divide How 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.

26.2 - m2) 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 18th 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) = 4 + 84 – 14 = 74

Ex) b2z-2bz+z2 for b = 6 and z =2

Answer: 52

Combine Like Terms

Simplify the Expressions by adding or subtracting Like terms.

Example: 3x2 -9xy + 2 +4x2 -13x2 -9xy + 2 +4x2 -1

Answer: 7x2 -9xy -1

Like versus Unlike

4xy2 and -7xy2

like 2xy2 and 2x2y

unlike 1 and -8

like 3x and (1/2)x

like 7xy and 4yx

like

Simplify the Following Expressions

x2 + 5x + 2y +7x2

Answer: 8x2 + 5x + 2y

b(5a2 -2a) -11a2b+2ab

Answer: -6a2b

Word Problemsa) 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 + 375b) How many total miles can she drive on one tank

of gas if she used 5 gallons on the highway?Answer: 20(5) + 375 = 475

Closure

Simplify the expression: -8x + 10x + 2(3-9x)

Evaluate when x = 2

Homework: Simplifying Expressions & Word Problems Packet