Video Lesson - Rational vs Irrational Numbers
On the Math test, integers and real numbers will appear far more often than any of
the other number types.
Even and Odd Numbers
Even numbers are those numbers that are divisible by two with no remainder.
included. Zero, however, is an integer and thus a member of the set.
Only integers can be even or odd, meaning decimals and fractions are not
. . . , –6, –4, –2, 0, 2, 4, 6, . . .
Odd numbers are those numbers not evenly divisible by two.
. . . , –5, –3, –1, 1, 3, 5, . . .
The set of even numbers and the set of odd numbers are mutually exclusive.
A more rigorous definition of even and odd numbers appears below:
Even numbers are numbers that can be written in the form 2n, where n
is an integer. Odd numbers are the numbers that can be written in the form 2n
+ 1, where n is an integer.
This definition is nothing more than a technical repetition of the fact that
even numbers are divisible by two, and odd numbers are not. It may come in
handy, though, when you need to represent an even or odd number with a variable.
Operations of Odd and Even Numbers
There are a few basic rules regarding the operations of odd and even numbers
that you should know well. If you grasp the principles behind the two types of
signed numbers, these rules should all come easily.
Addition:
even + even = even
odd + odd = even
even + odd = odd
Subtraction:
even – even = even
odd – odd = even
even – odd = odd
Multiplication and Division:
even × even = even
odd ×odd = odd
even × odd = even
Positive and Negative Numbers
Positive and negative numbers are governed by rules similar to those that have
to do with even and odd numbers. First, for their quick definitions:
Positive numbers are numbers that are greater than zero. Negative numbers are
numbers that are less than zero. The number zero is neither positive nor
negative.
Operations of Positive and Negative Numbers
The following rules define how positive and negative numbers operate under
various operations.
Addition and Subtraction:
When adding and subtracting negative numbers, it helps to remember the
following:Adding a negative number is the same as subtracting its opposite. For example:
3 + (-2) = 3-2 = 1
Subtracting a negative number is the same as adding its opposite. For example: 3 - (-2) = 3 + 2 = 5
Multiplication:
positive × positive = positive
negative × negative = positive
positive ×negative = negative
Division:
positive ÷positive = positive
negative÷ negative = positive
positive÷negative = negative
The rules for multiplication and division are exactly the same since any
division operation can be written as a form of multiplication: a ÷ b =
a/b = a × 1/b.
Absolute Value
The absolute value of a number is the distance on a number line between that
number and zero. Or, you could think of it as the positive “version” of every
number. The absolute value of a positive number is that same number, and the
absolute value of a negative number is the opposite of that number.
Video Lesson - Absolute Value Equations
The absolute value of x is symbolized by |x|.
Solving an equation with an absolute value in it can be particularly tricky. As
you will see, the answer is often ambiguous. Take a look at the following
equation
4 |
x|+ 2 = 10
We can simplify the equation in order to isolate |x|:
Knowing that |x| = 2 means that x
= 2 and x = –2 are both possible solutions to the
problem. Keep this in mind; we’ll deal more with absolute values in equations
later on in the Algebra chapter.
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Mathematics Practice Questions
Video Lessons and 10 Fully Explained Grand Tests
Large number of solved practice MCQ with explanations. Video Lessons and 10 Fully explained Grand/Full Tests.