MATH 3339 COMPREHENSIVE EXAM STUDY
GUIDE WITH COMPLETE SOLUTIONS
●● Ordinal numbers
Answer: numbers that describe position or order (first, second . . .)
●● Base 10
Answer: Also known as decimal system or denary system. Each digit in
a position can have a number from 0 to 9.
●● Whole Numbers
Answer: Natural numbers and zero (0, 1, 2, 3)
●● Integers
Answer: Whole numbers and their corresponding negatives (0..-3,-2,-
1,0,1,2,3...)
●● Natural Numbers
Answer: those numbers we typcally use to count 1,2,3
●● Fractions
,Answer: Portions of integers, expressed with a numerator and a
denominator 1/4, 1/2, etc)
●● Decimals
Answer: Portions of integers, expressed as numbers following a decimal
point (0.5, 0.67, etc).
●● Even Numbers
Answer: Integers divisible by two (...-6, -4, -2, 2, 4, 6)
●● Odd numbers
Answer: integers that are not divisible by two (...-7, -5, -3, 3, 5 etc)
●● Rational Numbers
Answer: are all integers and fractions
●● Irrational Numbers
Answer: any numbers that cannot be expressed as fractions, such as an
infinite, non-repeating decimal
●● 0
Answer: The sum of a number and its additive inverse
,●● Order of Operations
Answer: PEMDAS- Parenthesis, exponents, Multiplication, Division,
Addition, and Subtraction. Please excuse my dear aunt sally
●● Step 1: Order of operations
Answer: P: Parentheses - do everything in parentheses first. If there is
more than one operation inside the parentheses do PEMDAS order
●● Step 2: Order of operations
Answer: E: Exponents - deal with any exponents next (squared)
●● Step 3: Order of operations
Answer: M/D: Multiply and divide. This can be done in the same step as
one another.
●● Step 4: Order of operations
Answer: A/D: Addition & Subtration. This can be done in the same step
as one another.
●● Factors
Answer: whole numbers that are multiplied together to get a product.
Ex: The factors of 16 are 1, 2, 3, 8 & 16.
, The process of breaking a # down is factoring
Whole numbers can be classified by how many factors they have as
either being prime or composite numbers
●● Factor tree
Answer: A diagram showing the prime factorization of a number. The
factors branch out from the previous factors until all of the factors are
PRIME NUMBERS.
●● Prime Number
Answer: #'s (other than 0 & 1) that have only two factors, themselves
and 1.
Ex: 2, 3, 4, 5, 7, 11...
●● Composite Numbers
Answer: any positive integers that are not prime, meaning they have
more than two factors.
4, 6, 8, 9, 10...
●● Greatest Common Factor (GCF)
GUIDE WITH COMPLETE SOLUTIONS
●● Ordinal numbers
Answer: numbers that describe position or order (first, second . . .)
●● Base 10
Answer: Also known as decimal system or denary system. Each digit in
a position can have a number from 0 to 9.
●● Whole Numbers
Answer: Natural numbers and zero (0, 1, 2, 3)
●● Integers
Answer: Whole numbers and their corresponding negatives (0..-3,-2,-
1,0,1,2,3...)
●● Natural Numbers
Answer: those numbers we typcally use to count 1,2,3
●● Fractions
,Answer: Portions of integers, expressed with a numerator and a
denominator 1/4, 1/2, etc)
●● Decimals
Answer: Portions of integers, expressed as numbers following a decimal
point (0.5, 0.67, etc).
●● Even Numbers
Answer: Integers divisible by two (...-6, -4, -2, 2, 4, 6)
●● Odd numbers
Answer: integers that are not divisible by two (...-7, -5, -3, 3, 5 etc)
●● Rational Numbers
Answer: are all integers and fractions
●● Irrational Numbers
Answer: any numbers that cannot be expressed as fractions, such as an
infinite, non-repeating decimal
●● 0
Answer: The sum of a number and its additive inverse
,●● Order of Operations
Answer: PEMDAS- Parenthesis, exponents, Multiplication, Division,
Addition, and Subtraction. Please excuse my dear aunt sally
●● Step 1: Order of operations
Answer: P: Parentheses - do everything in parentheses first. If there is
more than one operation inside the parentheses do PEMDAS order
●● Step 2: Order of operations
Answer: E: Exponents - deal with any exponents next (squared)
●● Step 3: Order of operations
Answer: M/D: Multiply and divide. This can be done in the same step as
one another.
●● Step 4: Order of operations
Answer: A/D: Addition & Subtration. This can be done in the same step
as one another.
●● Factors
Answer: whole numbers that are multiplied together to get a product.
Ex: The factors of 16 are 1, 2, 3, 8 & 16.
, The process of breaking a # down is factoring
Whole numbers can be classified by how many factors they have as
either being prime or composite numbers
●● Factor tree
Answer: A diagram showing the prime factorization of a number. The
factors branch out from the previous factors until all of the factors are
PRIME NUMBERS.
●● Prime Number
Answer: #'s (other than 0 & 1) that have only two factors, themselves
and 1.
Ex: 2, 3, 4, 5, 7, 11...
●● Composite Numbers
Answer: any positive integers that are not prime, meaning they have
more than two factors.
4, 6, 8, 9, 10...
●● Greatest Common Factor (GCF)
