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Interactive Study Guide for Students: Pre-Algebra
Chapter 1: The Tools of Algebra
Section 1: Using a Problem-Solving Plan
Four-Step Problem Solving Plan
Examples
E______________: Read problem, ask questions
Weight(oz)
Cost
P______________: Reread, determine, make plan, estimate
1
$0.34
S______________: Use plan, revise
2
$0.55
E______________: Check solution, try again if necessary
3
$0.76
A ____________________ is an educated guess. When you
make a conjecture based on a pattern of examples or past
events, you are using _____________ ________________.
4
$0.97
5
$1.18
1. How much would it cost to mail a 9ounce letter?
2. Find the next term in
1,3,9,27,81,_____
3. Draw the next figure in the pattern:
Choose the Method of Computation
This is an _________________ step in solving
_________________.
Do you need
an exact answer?
Do you see a pattern
or number fact?
Use mental math
no
no
Estimate
Are there simple
calculations to do?
4. Ryan needs to save $125 for a ski trip.
He has $68 in his bank. He receives $15
allowance and earns $25 delivering
newspapers and $16 shoveling snow.
Does he have enough money for the
trip?
Use paper and pencil
Interactive Study Guide for Students: Pre-Algebra
Chapter 1: The Tools of Algebra
Section 2: Numbers and Expressions
Order of Operations
P
E
M
D
A
S
Examples
1. 3 + 4  5 =
2. 18  3  2 =
____________: symbols, usually letters, used to represent unknown
quantities.
3. 6(2 + 9) – 3  8 =
________________ Expressions: mathematical expressions that
contain at least one variable.
4. [(15 – 9) + 8(2)] =
5.
53  15
=
17  13
Translate Verbal Phrases into Numerical Expressions
Translate into expressions:
It is sometimes necessary to change a ____________ phrase into a
________________ expression. This is actually how ________ is used
in _____________.
6. The product of eight and
seven
7. The difference of nine and
three
Interactive Study Guide for Students: Pre-Algebra
Chapter 1: The Tools of Algebra
Section 3: Variables and Expressions
Evaluate Expressions
A ________________ is a placeholder for any value. This variable
represents some _____________ number.
An ____________________ expression contains sums and/or
products of variables and numbers. Example: x + 3
Replacing a variable with a number demonstrates the
_____________________ Property of Equality
Examples
1. Evaluate x + y – 9 if x=15
and y=26.
Evaluate each expression if
k=2, m-7, and n=4
2. 6m – 3k
3.
mn
2
4. n + (k + 5m)
Translate Verbal Phrases
The first step in translating verbal phrases into algebraic phrases is to
____________ a ___________.
Translate each phrase into an
algebraic expression:
5. twelve points more than
the Dolphins scored
6. four times a number
decreased by six
Interactive Study Guide for Students: Pre-Algebra
Chapter 1: The Tools of Algebra
Section 4: Properties
Properties of Addition and Multiplication
In algebra, _______________ are statements that are true for any
numbers.
Property
Addition
Multiplication
C_______________
a+b=b+a
ab = ba
A_______________
(a+b)+c=a+(b+c)
(ab)c = a(bc)
I________________
a+0=a=0+a
a1 = a = 1a
I________________
a+(-a)=0=(-a)+a
If a≠0, a1/a=1=1/aa
a(b+c)=ab+ac and (b+c)a=ba+ca
One way to show that something is not true is to provide a
_____________________.
2. (a  6)  5 = a  (6  5)
3. 0  12 = 0
4. Find 4  (25  11) mentally
5. Is the statement
“Subtraction of whole
numbers is associative” true
or false? If it is false, provide
a counterexample.
Simplify each expression: 6.
(k + 2) + 7
Simplify Algebraic Expressions
When you are asked to _________________ an algebraic expression,
that means to write it in a simpler form. You can use all of the
properties to help you.
Interactive Study Guide for Students: Pre-Algebra
Chapter 1: The Tools of Algebra
Name the property shown by
each statement:
1. 3 + 7 + 9 = 7 + 3 + 9
For any real numbers a, b, and c:
D_______________
Examples
7. 5  (d  9)
Section 5: Variables and Equations
Equations and Open Sentences
A mathematical sentence that contains an _________ sign is called an
equation.
Examples: 3 + 5 = 8 x – 7 = 14 2m = 6
An equation that contains a variable is an _______________
______________. An open sentence is neither ________ nor
_____________.
Examples
Solve:
1. If 12 – m = 8. does m=2, 4,
or 7?
2. Which value is the solution
of 2x+1=7?
a. 6 b. 5 c. 4 d. 3
A value for the variable that makes the equation true is called the
____________. The process of finding a solution is called
____________ the _____________.
Solve each equation mentally:
3. 5x = 30
S________________
T________________
If a=b then b=a
If a=b and b=c
then a=c
If 10=4+6 then 4+6=10
If 3+5=8 and 8=24
then 3+5=24
4.
72
9
d
Name the property of equality
shown:
5. If 5=x+2 then x+2=5
6. If y+8=15 and 15=7+8 then
y+8=7+8
Translate Verbal Sentences into Equations
Just as verbal phrases can be translated into algebraic expressions,
verbal sentences can be translated into ___________ and then
_______________.
Interactive Study Guide for Students: Pre-Algebra
Translate the sentence into an
equation then solve.
7. The difference of a number
and ten is seven. Find the
number.
Chapter 1: The Tools of Algebra
Section 6: Ordered Pairs and Relations
Ordered Pairs
Examples
In mathematics, a ________________ ______________ is used to
locate points. It is sometimes call the _________ ________.
Graph each ordered pair on
the coordinate system to the
left.
Draw arrows to the correct part:
1. (4, 1)
y-axis
origin
x-axis
M
N
P
2. (3, 0)
Write the ordered pair that
names the points on the
graph at the left.
3. M
4. N
5. P
An ______________ __________ of numbers is used to locate any
point of a coordinate plane. The first number is called the _______________ and the second is called the
________________. It is written like this ( ___, ___).
To ______________ and ordered pair, draw a _____ at the point that
corresponds to the ordered pair. The _____________ are you
directions to locate that point.
Relations
A set of ordered pairs such as {(1, 2), (3, 4), (4, 5)} is a
_________________. The ______________ of the relation is the set
of all of the numbers in the __-_____________. The ______________
of the relation is the set of all of the numbers in the _______________.
A relation can be shown as ordered _______, in a ___________, or on
a ______________.
6. Express the relation
{(0,0),(2,1),(1,3),(5,2)}as a
table and as a graph.
x
y