REAL

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REAL NUMBERS
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If you were asked to count, the numbers youd say
are called counting numbers. These numbers can
be expressed using set notation.
These are also called the natural numbers.
1, 2, 3, 4, . . .
If we include 0 we have the set of whole numbers.
0, 1, 2, 3, 4, . . .
, -3, -2, -1, 0,1, 2, 3, . . .
Include the opposites of the whole numbers and
you have the set of integers.
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Whole numbers are a subset of integers and
counting numbers are a subset of whole numbers.
This means to divide one integer by another or
make a fraction
If we express a new set of numbers as the
quotient of two integers, we have the set of
rational numbers
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There are numbers that cannot be expressed as the
quotient of two integers. These are called
irrational numbers.
REAL NUMBERS
rational numbers
irrational numbers
The rational numbers combined with the irrational
numbers make up the set of real numbers.
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Translating English to Maths
a b
a - b
ab

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ORDER OF OPERATIONS
When there is more than one symbol of operation
in an expression, it is agreed to complete the
operations in a certain order. A mnemonic to
help you remember this order is below.
Apply Indices
Complete multiplication and division from left to
right
Complete addition and subtraction from left to
right
Do any simplifying possible inside of brackets
starting with innermost brackets and working out
rackets
ultiplication
ndices
ivision
ddition
ubtraction
B I M D A S
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complete addition and subtraction, left to
right
brackets combine these first
indices apply the indice now
complete multiplication and division, left to
right
BIMDAS
BIMDAS
BIMDAS
BIMDAS
BIMDAS
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COMMUTATIVE PROPERTY
The operations of both addition and
multiplication are commutative
When adding, you can commute or trade the terms
places
When multiplying, you can commute or trade the
factors places
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ASSOCIATIVE PROPERTY
The operations of both addition and
multiplication are associative
When adding, you can associate and add any
terms first and then add the other term.
When multiplying, you can associate and
multiply any factors first and then multiply the
other factor.
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DISTRIBUTIVE PROPERTY
The operation of multiplication distributes over
addition
The distributive property also holds for a factor
that is multiplied on the left.
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CAUTION Remember that the value for a and/or b
could also be positive or negative.
Rules of Signs
A positive times a negative is
A negative times a positive is
NEGATIVE
NEGATIVE
The negative of a negative
POSITIVE
A negative divided by a positive is
NEGATIVE
A positive divided by a negative or
A negative divided by a negative is
POSITIVE
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Acknowledgement I wish to thank Shawna Haider
from Salt Lake Community College, Utah USA for
her hard work in creating this PowerPoint. www.sl
cc.edu Shawna has kindly given permission for
this resource to be downloaded from
www.mathxtc.com and for it to be modified to suit
the Western Australian Mathematics Curriculum.
Stephen Corcoran Head of Mathematics St
Stephens School Carramar www.ststephens.wa.edu.
au