Transcript 1.2-1.3 2015 Simplifying algebraic expressions

Warm Up
Evaluate each expression.
1. –x2 for x = -5
2. 5x2 – x – 3x for x = -2
Simplify each expression.
3. -3(2x - y)
4. 4 - (x + y)
Success Criteria:
I can classify a variable
I can graph numbers on a number
line
I can order real numbers
I can use order of operations
1.
2.
3.
4.
5.
6.
Do Now
Check HW #1
Log on to pearson book
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HW - Go through expression
solving ppt attached to
website
Vocabulary
• Pg 11 copy into the next section of your
notebook with word, definition, and
example.
The diagram shows some important subsets of the
real numbers.
There are three different ways in which a
basketball player can score points during a game.
There are 1-point free throws, 2-point field goals,
and 3-point field goals. An algebraic expression
can represent the total points scored during a
game.
To translate a real-world situation into an
algebraic expression, you must first determine
the action being described. Then choose the
operation that is indicated by the type of action
and the context clues.
Action
Combine
Combine equal
groups
Separate
Separate into
equal groups
Operation
Add
Possible Context Clues
How many total?
Multiply
How many altogether?
Subtract
How many more? How
many remaining?
Divide
How many in each group?
Example 1: Translating Words into Algebraic
Expressions
Write an algebraic expression to represent each
situation.
A. the number of apples in a basket
of 12 after n more are added
12 + n
Add n to 12.
B. the number of days it will take to
walk 100 miles if you walk M miles
per day
Divide 100 by M.
C. Lucy’s age y years after her 18th birthday
18 + y
Add y to 18.
D. the number of seconds in h hours
3600h
Multiply h by 3600.
Shhh do this in your head!
20 ÷ 10 (2) + 3(2) ÷ 3
To evaluate an algebraic expression,
substitute a number for each variable and
simplify by using the order of operations.
One way to remember the order of
operations is by using the mnemonic
PEMDAS.
Order of Operations
1.
2.
3.
4.
Parentheses and grouping symbols.
Exponents.
Multiply and Divide from left to right.
Add and Subtract from left to right.
Example 2A: Evaluating Algebraic Expressions
Evaluate the expression for the given values
of the variables.
2x – xy + 4y for x = 5 and y = 2
2(5) – (5)(2) + 4(2) Substitute 5 for x and 2 for y.
10 – 10 + 8
0+8
8
Multiply from left to right.
Add and subtract from left to right.
x2y – xy2 + 3y for x = 2 and y = 5.
(2)2(5) – (2)(5)2 + 3(5) Substitute 2 for x and 5 for y.
4(5) – 2(25) + 3(5)
20 – 50 + 15
–15
Evaluate exponential expressions.
Multiply from left to right.
Add and subtract from left to right.
Recall that the terms of an algebraic expression
are separated by addition or subtraction
symbols. Like terms have the same variables
raised to the same exponents. Constant terms
are like terms that always have the same value.
Remember!
Terms that are written without a coefficient have
an understood coefficient of 1.
x2 = 1x2
Example 3A: Simplifying Expressions YOU TRY!
Simplify the expressions.
3x2 + 2x – 3y + 4x2
Identify like terms.
3x2 + 2x – 3y + 4x2
7x2 + 2x – 3y
Combine like terms.
3x2 + 4x2 = 7x2
j(6k2 + 7k) + 9jk2 – 7jk
6jk2 + 7jk + 9jk2 – 7jk
15jk2
Distribute, and identify like terms.
Combine like terms.
7jk – 7jk = 0
Check It Out! Example 4a
A travel agent is selling 100 discount packages.
He makes $50 for each Hawaii package and $80
for each Cancún package.
Write an expression to represent the total the
agent will make selling a combination of the
two packages.
Let h be the number of Hawaii packages.
Then 100 – h is the remaining Cancun packages.
50h + 80(100 –h) = 50h + 8000 –80h Distribute 80.
= 8000 – 30h
Combine like terms.
Check It Out! Example 4b
How much will he make if he sells 28
Hawaii packages?
Evaluate 8000 –30h for h = 28.
8000–30(28) = 8000–840
= 7160
He will make $7160.
Assignment #2
Pg 22-24 #12 - 51 x3, 52, 53
Don’t forget syllabus
Tuesday!
#2
Pg 22-24 #12 - 51 x3 skip 45 (13 pts)
Lesson Quiz: Part I
Write an algebraic expression to represent
each situation.
1. the number of cards in a 52-card deck after n
cards are dealt. 52 – n
2. the number of days in W weeks 7W
3. Evaluate: rq2 + 3qr + r2 for r = 5 and q = 2. 75
4. Simplify: 5h2 + 4k + 7h – 4h2. h2 + 4k + 7h
Lesson Quiz: Part II
Jake has only nickels and dimes in his
pocket.
5. Write and simplify an expression for the
total value if Jake has 20 coins.
Possible answer: $2 – ($0.05)N
6. How much does he have if he has 7 nickels?
$1.65