Post on 22-Dec-2015
transcript
REAL
NUMBERS
{1, 2, 3, 4, . . . }
If you were asked to count, the numbers you’d say are called counting numbers. These numbers can be expressed using set notation.
These are also called the natural numbers.
{0, 1, 2, 3, 4, . . . }If we include 0 we have the set of whole numbers.
{ …, -3, -2, -1, 0,1, 2, 3, . . . }
Include the opposites of the whole numbers and you have the set of integers.
rational numbers
Whole numbers are a subset of integers and counting numbers are a subset of whole numbers.
integers
whole numbers
counting numbers
If we express a new set of numbers as the quotient of two integers, we have the set of rational numbers
This means to divide one integer by another or “make a fraction”
rational numbers
There are numbers that cannot be expressed as the quotient of two integers. These are called irrational numbers.
integers
whole numbers
counting numbers
2
irrational
numbers
The rational numbers combined with the irrational numbers make up the set of real numbers.
REAL NUMBERS
Translating English to Maths
sum of two numbers
difference between two numbers
The product of two numbers
the quotient of two numbers
is =
ab
a - b
a + b
ba
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.
B I M D A Srackets
ndicesultip
lication
ivisiondditio
n
ubtraction
Do any simplifying possible inside of brackets starting with innermost brackets and working out
Apply IndicesComplete multiplication and division from left to rightComplete addition and subtraction from left to right
423532 2
BIMDASBIMDAS
brackets – combine these first
42322 2
BIMDAS
indices – apply the indice now
42342
BIMDAS
complete multiplication and division, left to right
468
BIMDAS
complete addition and subtraction, left to right
10
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COMMUTATIVE PROPERTY
The operations of both addition and multiplication are commutative
abba 3223 When adding, you can “commute” or trade the terms places
abba 3223
When multiplying, you can “commute” or trade the factors places
ASSOCIATIVE PROPERTY
cbacba 321321
When adding, you can “associate” and add any terms first and then add the other term.
cbacba 432432
When multiplying, you can “associate” and multiply any factors first and then multiply the other factor.
The operations of both addition and multiplication are associative
DISTRIBUTIVE PROPERTY
The operation of multiplication distributes over addition
acabcba 4323423
The distributive property also holds for a factor that is multiplied on the left.
acabacb
2423243
abba A positive
times a negative is
NEGATIVE
abba A negative
times a positive is
NEGATIVE
aa The negative of a negative
POSITIVE
CAUTION: Remember that the value for a and/or b could also be positive or negative.
b
a
b
a
b
a
A positive
divided by a negative or
A negative divided by a positive is
NEGATIVE
b
a
b
a
A negative
divided by a negative is POSITIVE
Acknowledgement
I wish to thank Shawna Haider from Salt Lake Community College, Utah USA for her hard work in creating this PowerPoint.
www.slcc.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 CorcoranHead of MathematicsSt Stephen’s School – Carramarwww.ststephens.wa.edu.au