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Ch. 1-1 Algebraic Expressions and the Order of Operations
Algebra Map
In the concept map below, various aspects of algebra are found,
as well as how the aspects relate to different parts of "language"
such as nouns, verbs, and pronouns.
Different Ways to Show Multiplication:
"X" (times sign)
3x5
" . " (raised dot)
3 . 5
* (asterisk, used with computers)
3*5
(#)(#) parentheses
(3)(5)
# next to letter
3x = (3)(x)
letter next to letter
xyz = x (y)(z)
exponents
23 = 2 x 2 x 2
Different Ways to Show Division:
Division symbol ( ÷)
2÷5
Slash symbol ( / )
2/5
Fraction bar
2
5
Ch. 1-1 Algebraic Expressions and the Order of Operations
-a variable is a symbol that stands for one or more numbers
Example:
x=2
y = -4
z=0
-an algebraic expression is a mathematical phrase that uses numbers
variables and operation symbols.
Example:
x+2
y–2
4x
You can translate word phrases into algebraic expressions.
3 more than a number
A number increased by 3
x+3
The quotient of a number
and 8
x/8
6 times a number
The product of 6 and a
number
6x
15 less than a number
15 subtracted from a
number
x - 15
•Less... Less than... Is Less Than
Be cautious when you are translating to be exact, especially with the word phrases: "Less, Less than, and Is less than." Read the follow
Common words used in English:
Addition
Subtraction
Multiplication
Division
Sum
Plus
Added to
More*, More
than*
Increased by
Total, totaling
Difference
Minus
Subtracted from
Less*
Less than *
Decreased by
Product
Times
Multiply
Twice, Double ( x 2)
Triple ( x 3 )
Of
Quotient of
Divided by
Into
Per
Five less a number is two.
Five less than a number is two.
Five is less than a number.
5-n=2
n-5=2
5<n
variable
A symbol that stands
for one or more
numbers, like a
pronoun
x = slope
of a line
h = height
z = 22
t = -55
Algebraic
expression
mathematical phrase
that uses numbers
variables and
operation symbols, like
an incomplete
sentence
y–2
x+2
4x
Numerical expression
mathematical phrase
that uses numbers and
operation symbols, like
an incomplete
sentence
5–2
2+2
4x8
Example 1: Write an algebraic expression for each statement below.
a.) At a ballpark, team hats are $15 each. Let n represent the number of
hats purchased.
15n
b.) You lose $5 from your wallet. Let x represent the original amount of
money that you started with.
x-5
-to simplify an expression means to replace each variable with its simplest
name
-to evaluate an expression, replace each variable with a number and then
simplify
Simplify
means to replace each
variable with its
simplest name
25y – 5y
Simplified is
20y
4t x 8
Simplified
is 32t
5x + 2x
Simplified is
7x
Evaluate
n=4
replace each variable
with a number and
then simplify
n+5=
9
6n =
24
n/4 =
1
Get out
whiteboards –
Going to
practice 
1. 5 less than a number n
n -5
|n| + 15
2. 15 more than the absolute value of a number
60n
3. The number of minutes in n hours
4. 5 more than a number, divided by 9
(x+5) / 9 or as a fraction
5. 3 more than the product of 8 and a number
6. 3 less than the absolute value of a number, times 4
8y +3
4 ( |n| +3 )
7. The amount of money Waldo has if he has $10 more than Jon
J +10
8. The amount of money that Mika has is she has some quarters
.25q
9. How much weight Kirk can lift if he lifts 30lb more than his
brother
W +30
10.How fast Rya runs if she runs 5 mi/hr slower than Danae
d-5
1. N / 4
A number divided by four
The quotient of a number and
four
2. n + 4
4 more than a number
The sum of a number and 4
A number increased by 4
3. 3n
The product of 3 and a number
Tripled a number or a number tripled
3 times a number
4. N - 8
8 less than a number
The difference of a number and 8
A number decreased by 8
Order of Operations: Basically "4" Rules (Do the rules in order):
RULE 1 - Do all operations within grouping symbols (parentheses,
brackets, vinculum (fraction bar))
RULE 2 - Evaluate the number value for any exponents
RULE 3 - Multiply or divide in order from left to right
RULE 4 - Add or subtract in order from left to right
Example 3: Use the order of operations to simplify each expression below.
x = 4 and y = 2
a.) (x + 4) – 5 + x * 3
b.) 2y – x + 8/y
Plug in for x and y
(4 + 4) – 5 + 4 * 3
Plug in for x and y
2(2) – 4 + 8/2
Simplify using order of operations
(8) – 5 + 12 = 15
c.) xy/2 + 5 – 3
Plug in for x and y
4(2)/2 + 5 - 3
Simplify using order of operations
8/2 + 5 – 3 = 6
Simplify using order of operations
4–4+4=4
d.) 18 – 3y + (x – 2)
Plug in for x and y
18 – 3(2) + (4 – 2)
Simplify using order of operations
18 – 6 + 2 = 14
Example:
When there are two or more parenthesis, or grouping
symbols, perform the inner most grouping symbol first.
2 + 3[ 5 + (4 - 1)2]
2 + 3[ 5 + (3)2] inner most parentheses are done first
2 + 3[ 5 + 9] then work your way out
2 + 3[ 14]
2 + 42
44
Classwork – Textbook p 7 1-5
C3 Section 1.1
Homework– Textbook page 7-8;
6-24 evens show work for each
problem or no points
Problems 6, 8, 18 do not need to
show work put a circle around the
problem number