By the end of this lesson you will be able to explain and calculate the following: 1. A Rational Number 2. An Irrational Number 3. Order of Operations

 We use numbers such as integers, fractions and decimals every day.  They form part of what is called the Real Number System.  Real numbers  Real numbers can be divided into two categories  rational numbers and  irrational numbers

 The set of real numbers is a collection that contains natural, integer, rational and irrational numbers.  Let us first define each of these sets and see their relationship to each other.

 Anton has calculated the answer to × 4 as 44  Marco insists that the answer is 29.  Who is correct?  The order of operations requires that: 1.all expressions in brackets are evaluated first, beginning with the innermost pair of brackets 2.then, all multiplication and division are evaluated, working from left to right 3.and finally, any addition and subtraction, working from left to right.

This is our start number This is the direction of move This is the number of places we need to move =1

This is our start number This is the direction of move This is the number of places we need to move =-7

= 1 -4 – 6 = -10

A I S S I D and Now.…there is one more thing we need to know. Remembering AIS and SID can help us with this next stage.

= Look at the signs in the middle, if they are the same, then replace them with

= 3 +

= Look at the signs in the middle, if they are different, then replace them with

=

Can you use all your knowledge of negative numbers so far to find the answer to these calculations? = = Remember: This is your start number and the new sign in the middle is the direction - +

 When multiplying integers, the following rules are obeyed. a) Positive × Positive = Positive 5 × 8 = 40 b) Positive × Negative = Negative 5 × −8 = −40 c) Negative × Positive = Negative −5 × 8 = −40 d) Negative × Negative = Positive −5 × −8 = 40  When dividing integers, use the same rules a) Positive ÷ Positive = Positive 16 ÷ 2 = 8 b) Positive ÷ Negative = Negative 16 ÷ −2 = −8 c) Negative ÷ Positive = Negative −16 ÷ 2 = −8 d) Negative ÷ Negative = Positive −16 ÷ −2 = 8

 When multiplying and dividing integers:  like signs give positive answers,  unlike signs give negative answers.