Contents
Glossary
Review of first one hundred
Idea of a number
Addition
The commutative law of addition
Exercise 1
A number has many names
Exercise 2
Subtraction
Set
Exercise 3
Multiplication
The commutative law of multiplication
Exercise 4
Division by a single digit
Exercise 5
Review of the base ten system of notation
The meaning and reading of large numbers
Exercise 6
Expanded numerals
Exercise 7
Addition of large numbers
Exercise 8
Subtraction of large numbers
Exercise 9
Multiplication of large numbers
Checking of multiplication
Exercise 10
Division by a single-digit divisor
The concept of "long division"
Zero in the quotient
Division by multiple-digit divisors
Exercise 11
Divisibility of numbers
Exercise 12
Prime and composite numbers
Prime numbers
Definition of prime numbers
Infinite number of prime numbers
Exercise 13
Exercise 25
Base two system of notation
Exercise 26
Changing a base ten numeral to its
equivalent base two numeral
Exercise 27
Changing a binary numeral to its
equivalent base ten numeral
Exercise 28
Addition of binary numerals
ALGEBRA
Classification of numbers
Definition of terms
Positive and negative signs to indicate
difference in number’s quality
Exercise 29
Exercise 30
Rational numbers
Exercise 31
Summary
Addition of signed numbers
Addition of numbers with unlike signs
Summary
Exercise 32
Subtraction of signed numbers
Summary of the idea of negative numbers
Parentheses
Exercise 33
Exercise 35
Exercise 36
Multiplication and division of
signed numbers
Expressing a composite number
as a product of its prime numbers
Summary of prime and composite numbers
Exercise 14
Factors
Idea of a factor
Prime factors
Exercise 15
Common factors
The greatest common factor (GCF)
Finding the GCF of two or more numbers
Summary of the concept of a factor
Exercise 16
Multiple
Common multiple
Least common multiple (LCM)
Finding the LCM of two or more numbers
Exercise 17
Exponents
A product and its factors
Exercise 18
Order of operations with exponents
Exercise 19
Law of exponents
Exercise 20
Exercise 21
Scientific notation for large numbers
Negative exponents
Scientific notation summary
Rising a fraction to a given power
Exercise 22
Integers
Square roots
Definition of terms
Exercise 23
Math terms and their meanings
Perfect squares
Cube roots
Definition of terms
Perfect cubes
Exercise 24
Pythagorean Theorem
Rule of signs
Exercise 37
Exercise 38
Exercise 39
Algebraic number symbols
Three fundamental math laws
Definitions
Evaluating expressions
Basics of addition and subtraction of algebraic terms
Basics of multiplication and division of algebraic terms
Simplifying algebraic expressions
Exercise 40
The algebraic equation
Definition of algebraic equation
Solving the equation
Exercise 41
Algebraic axioms
Two fundamental algebraic axioms
Exercise 42
Solving equations by transposition of the terms
Exercise 43
Solving an equation with two or
more terms
Exercise 44
Exercise 45
Exercise 46
Exercise 47
Answers
Index