Evaluate and simplify algebraic expressions by substituting and using order of operations How to You will need to translate words into mathematical operations What are some words or phrases for ID: 605663
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Slide1
1-3 Algebraic Expressions
Evaluate and simplify algebraic expressions by substituting and using order of operations.Slide2
How to…
You will need to translate words into mathematical operations.
What are some words or phrases for:
Addition
Subtraction
Multiplication
DivisionSlide3
Practice
Ex: The
product of 9 and
b
9b
26 less than
12 (**when you see “less than” notice that the first number goes last)
12 - 26
You try:
The quotient of 6 and 3
6 more than twice the points
T
wo times the sum of a and bSlide4
Modeling a Situation
You start with $20 and save $6 each week. What algebraic expression models the total amount you save?
What do we know?
How can we make an algebraic expression using what we know?
20 + 6wSlide5
Evaluate an Algebraic Expression
Replace variables with values
Use order of operations to simplify
Ex: q + r – 15 if q = 21 and r = 18
21 + 18 -15
39 – 15
24Slide6
Simplifying Expressions
Combine like terms
Use commutative property
Combine
If there is any distributing to be done
…
distribute FIRST!
Slide7
1-4 Solving Equations
Solve problems by writing equations.Slide8
Equation
An equation is a statement that two expressions are equal.
Equations have an equal sign, expressions do not.Slide9
Properties of Equality
Reflexive
:
a = a
Ex: 5 = 5
Symmetric
: If
a = b,
then
b = a
Ex: If ½ = 0.5, then 0.5 = ½
Transitive: If a = b and b = c, then a = cEx: If 2.5 = and , then Substitution: If a = b, then you can replace a with b and vice versa.Ex: If a = b and 9 + a = 15, then 9 + b = 15 Slide10
Solving
A
solution of an equation
is a value that makes the equation true.
To find a solution, use
inverse operations
to “undo” the equation.
Must be done to BOTH sides of the equation.
If there is distributing to do, do it first.
Next, undo any addition or subtraction.
Last, undo multiplication or division.
Ex: distribute add 27 subtract 3y divide by 3 Slide11
No Solution or Identities
Equations have
no solution
if all variables cancel and the statement is false.
Ex: 4 = 5 (there are no variables and we know that 4
5)
Equations have
infinitely many solutions
or are
identities
if all variables cancel and the statement is true.
Ex: 0 = 0 (notice the answer is not zero. We know that it is true that 0 = 0 so the equation is an identity) Slide12
Literal Equations
An equation that uses at least 2 different variables.
You solve for a variable “in terms of” the other variables.
Isolate one of the variables and get all others to the opposite side of the equal sign.
You Try:
The equation
relates temperatures in degrees Fahrenheit
F
and degrees Celsius
C
. What is
F in terms of C? multiply by the reciprocal add 32 Slide13
Assignment
Odds p.22 #13-21
p.30 #21-33