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Study Guide Chapter 1
**REVIEW CLASS NOTES **
Section 1-1
Translating Phrases into Algebraic Expressions and Translating Algebraic Expressions
into English
Keywords: Sum, Product, Quotient, Difference, Quantity, (commas)
- Each of these words require parentheses.
- If you do not use parentheses when these words occur you end up not using the
proper order of operations
- Commas are used to separate phrases; which mean they are also used to
separate math operations
***Remember that less than is different than less and it is also different than is less than
6 less than a number translates to x – 6
6 less a number translates to 6 – x
6 is less than a number translates to 6 < x
Variable:
letters or symbols used to represent unspecified numbers
Algebraic Expression:
one or more numbers and variables, along with one or more arithmetic operation
Numerical Expression:
only include constants (opposite of a variable)
Sequence:
a numerical pattern
Term:
each number or item in a sequence
Section 1-2
Order of Operations: PEMDAS
1. Parenthesis
Start with the inner most set of parenthesis and work out
2. Exponents
3. Multiply
Divide
GROUPED; Work from left to right
4. Addition
Subtraction
GROUPED; Work from left to right
**Multiplication/Division are grouped together and done as they appear from left to right.
Addition/Subtraction are also grouped and done after M/D
10 + 12 + 4 * 3
10 + 12 + 12
=34
**Start with the inner most set of parenthesis and work out
( 8 * 2 + (12 – 7 ) ) -1
( 8 * 2 + 5) -1
(16 + 5) -1
21 – 1
= 20
Vinculum
 Formal name for the dividing bar or fraction bar
 treat as a parenthesis during PEMDAS
 the vinculum tells you to divide when the numerator & denominator have been simplified
Section 1-3
Writing expressions using exponents:
Example:
Write 5*5*5*n*n*n*n*n
Solution:
Writing Algebraic Expressions:
Example:
Write an Algebraic Statement for the following:
Three less than twice a number
Solution: 2x – 3
Chapter 1, Section 3
Square Roots
The following table shows numbers and their squares.
You should know these.
MEMORIZE THEM!!!
#
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Squares 1
4
9
16
25
36
49
64
81
100
121
144
169
196
16
17
18
19
20
21
22
23
24
25
256
289
324
361
400
441
484
529
576
625
15
Squares 225
Section 1-4
Real Numbers and the Number Line
VOCAB:
Real Numbers:
{
ALL THE NUMBERS YOU HAVE EVER USED
}
Rational Numbers:
{
NUMBERS THAT MAKE SENSE AND REPEAT OR STOP
“YOU KNOW WHAT IS COMING NEXT”
Whole Numbers:
{
0 AND ALL COUNTING NUMBERS
Natural Numbers (Counting):
Start at 1 { ALL THE NUMBERS YOU CAN COUNT TO
Integers:
Whole numbers & their opposites {… -4, -3, -2, -1, 0, 1, 2, 3, 4 , …}
ESSENTIALLY NUMBERS YOU WOULD PUT ON # LINE
}
}
}
COMPARING NUMBERS ( <, =, > ) :
1. Negatives < Positives
2. Negatives < 0 < Positives
3. If Fractions with unlike denominators:
Method 1:
convert to a common denominator or LCD & then compare numerators
Method 2:
convert to a decimal with 3 decimal places & then compare numbers
Examples:
Fill in the appropriate symbol (<, =, >)
12 ? 27
5
13
Example:
Rank from least to greatest:
7
/13,
0.55,
denominator
0.538, 0.550,
9
/20
7
/13,
0.55,
9
/20
Convert Fraction to decimal—divide numerator by
0.450
Steps:
1. Convert to decimal
2. Rank (order)
3. Write in original form
0.450, 0.538,
0.550 Rank in order
9
0.550 Write in order in original form
/20,
7
/13,
Be careful when working with square roots. You need to find which integer the square root is approximately
equal to and go from there.