Welcome to GED Prep: M-1Basic Math : Welcome to GED Prep: M-1Basic Math This class will cover the following topics:
Whole Number Concepts
Number Line
Number Sets
Integers
Place Value
The Number Line : The Number Line A number line is a picture of a straight line with marks that show each number in order from the least to the greatest amount.
Number lines can help with basic operations and comparing numbers.
The arrow means that numbers in the set can go on forever.
Number Sets : Number Sets Natural Numbers: The set of natural numbers are the numbers used when counting such as 1, 2, 3, 4, 5……
Whole Numbers: This is the set of natural numbers but it includes the number zero.
0, 1, 2, 3, 4, 5, 6, 7……….
Number Sets : Number Sets Integers: This is the set of whole numbers and negative numbers.
A negative number has a value of less than zero.
Negative Numbers : Negative Numbers Negative Numbers can occur when a number represents an amount less than zero. Examples include a temperature of -5 or a bank balance of -$40.00.
Number Sets : Number Sets Rational Numbers: A rational number is any number that can be written as fraction (or a ratio).
Rational numbers include integers and decimals.
A rational number cannot have a zero as a quotient.
Examples of Rational Numbers : Examples of Rational Numbers Integers can be divided by one.
7/1 0/1 9/1 1000/1
You cannot divide an integer by zero so this is
NOT a rational number 8/0
Decimals can be expressed as fractions so
they are rational.
0.50 = ½ 3.75 = 3 75/100
Examples of Rational Numbers : Examples of Rational Numbers Algebra allows us to express repeating
decimals as fractions.
So even decimals that repeat over
and over are still rational numbers.
What if you cannot express a decimal as
a fraction????
Number Sets : Number Sets Some decimals do not repeat the same
numbers and they go on forever.
These numbers cannot be expressed as a
fraction and so they are called
Irrational Numbers.
Number Sets : Number Sets Algebraic Numbers: A number that is a root of a non-zero polynomial with rational coefficients.
This will be covered in my algebra classes.
A Transcendental Number is any number that is not algebraic.
Number Sets : Number Sets Real Numbers: The set of real numbers includes all integers, all rational and irrational numbers and all algebraic and transcendental numbers.
Number Sets : Number Sets Imaginary Numbers: Any number that gives a negative result when squared. Complex Numbers: A combination of real and imaginary numbers.
Place Value : Place Value The value of a digit depends on its place in
the number. Each place value is ten times
greater than the place to the right.
Place Value : Place Value Ones, Tens and Hundreds:
In the number 326, the 3 represents 3 sets
of 100, the 2 represents 2 sets of 10 and the
6 represents 6 sets of ones.
So in this example the three is in the
hundreds place, the 2 is in the tens place
and the 6 is in the ones place.
Place Value : Place Value When working with decimals, the place value goes tenths, hundredths, thousandths.
So the number 18.691 would have a one in the tens place, an eight in the ones place, a six in the tenths place, a nine in the hundredths place and a one in the thousandths place.
Now its your turn to try some examples!