sat readiness. simplifying algebraic expressions 1.4
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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
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