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REAL NUMBERS

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{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.

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rational numbers Whole numbers are a subset of integers and counting numbers are a subset of whole numbers. integers whole numberscounting 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”

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rational numbers There are numbers that cannot be expressed as the quotient of two integers. These are called irrational numbers. integers whole numberscounting numbers irrational numbers The rational numbers combined with the irrational numbers make up the set of real numbers. REAL NUMBERS

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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 b a

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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. B I M D A SB I M D A S rackets ndices ultiplication ivisionddition ubtraction Do any simplifying possible inside of brackets starting with innermost brackets and working out Apply IndicesComplete multiplication and division from left to right Complete addition and subtraction from left to right

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BIMDAS brackets – combine these first BIMDAS indices – apply the indice now BIMDAS complete multiplication and division, left to right BIMDAS complete addition and subtraction, left to right

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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 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. The operations of both addition and multiplication are associative

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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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A positive times a negative is NEGATIVE A negative times a positive is NEGATIVE The negative of a negative POSITIVE CAUTION: Remember that the value for a and/or b could also be positive or negative. A positive divided by a negative or A negative divided by a positive is NEGATIVE 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.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.www.mathxtc.com Stephen Corcoran Head of Mathematics St Stephen’s School – Carramar www.ststephens.wa.edu.au

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