Download 02-16 4.3 Order of Operations

§4.3 Order of
Operations
02/16/17
Today We’ll Discuss
How do we evaluate algebraic
expressions?
How do we use the order of operations?
Numerical Expression
Definition: A collection of numbers and
operation symbols is a numerical
expression.
Algebraic Expression
Definition: A collection of variables,
numbers, and operation symbols is an
algebraic expression.
To evaluate an algebraic expression is to
substitute a number for a variable and
evaluate the expression.
Algebraic Expression
“Take some number and add 4.”
x+4
Algebraic Expression
Evaluate x + 4 when x = 9.
x+4
Substitute
9 + 4 = 13
Example
a) Evaluate y ÷ 4 when y = 24.
b) Evaluate 7n when n = 3.
So… What Did You Intend to Say?
“I saw the man with the binoculars.”
“They are hunting dogs.”
“Police help dog bite victim.”
“Wanted: a nurse for a baby about twenty
years old.”
“I once saw a deer riding my bicycle.”
“Look at the dog with one eye.”
en.wikipedia.org/wiki/List_of_linguistic_example_sentences#Syntactic_ambiguity
So… What Did You Intend to Say?
“"Turn right after
going straight and
then left".”
So… What Did You Intend to Say?
6−4+2
So… What Did You Intend to Say?
6 − (4 + 2)
The Order of Operations
When reading a numerical expression, we
agree to perform operations in the
following order:
1) Perform operations inside Parentheses
2) Evaluate numbers with Exponents
3) Multiply and Divide from left to right
4) Add and Subtract from left to right
The Order of Operations
A “common” mnemonic for remembering
this order:
Example
Evaluate each expression using the order of
operations.
a) 17 − 4 • 2
d) 5 • 11 − 2
b) 12 + 12 ÷ 3
e) 92 − 1 + 4
c) 13 − (4 − 2)3 + 2
Example
Evaluate each expression using the order of
operations.
a) 17 − 4 • 2
d) 5 • 11 − 2
b) 12 + 12 ÷ 3
e) 92 − 1 + 4
c) 13 − (4 − 2)3 + 2 f) 15 − (28 ÷ (7 − 3))
Example
Evaluate each expression using the given
substitution.
a) 3(x + 4) when x = 6
b) 12 + n2 when n = 3
c) 9 + 3(y ÷ 4) when y = 12
Example
Write a numerical expression that uses the
order of operations to represent each problem.
a) Divide 33 by the sum of 8 and 3.
b) Subtract the difference of 6 and 4 from 12.
c) Add the square of 7 to the sum of 4 and 6.
Example
You work a part-time job that pays $11 an
hour. Write an algebraic expression that
represents the total amount of money
you’ve made in terms of hours worked.
Example
You have a part-time job that pays $16 per
hour. You receive a paycheck with a gross
amount of $512. How many hours did you
work?
Homework #9 - §4.3
Pages 150-153
#7, 9, 16, 18, 20, 24, 26, 28, 31,
39 (Just determine whether the answer
is correct or incorrect and why or why
not)