Chapter 2: Integers, Rational Numbers and Real Numbers

Section 2.1: Negative Numbers
The negative number –2 as negative 2, not minus 2 (‘negative’ is a state while ‘minus’ is an operation). For example, if you have $5 and you owe your friend $2, how much do you have left? Since nothing is mentioned about you returning money to your friend, you have $5 left. Thus $2 is a state of owing money. However, if you return $2 to your friend, you have $5 + (–$2) = $5 – $2 = $3 left, i.e. 5 minus 2 is an operation of returning money.

Section 2.2: Addition and Subtraction involving Negative Numbers

Key Concept 1: Adding a negative number is the same as subtracting the absolute value of the number,
e.g. 5 + (−2) = 5 − 2.
Key Concept 2: Subtracting a negative number is the same as adding the absolute value of the number,
e.g. 5 − (−2) = 5 + 2.

Section 2.3: Multiplication and Division involving Negative Numbers

We will start by trying to work out the answer to 7 × (-4).
First of all, think about the sum 7 × 4. The answer is 28.
This is the same as 7+7+7+7, which gives 28.
In the same way, the sum 7 × (-4) can be written (-7) + (-7) + (-7) + (-7), which gives -28.

Section 2.4: Rational Numbers and Real Numbers

Traditionally, real numbers are classified as either rational or irrational numbers. Another way to classify real numbers is according to whether their decimal forms are terminating, recurring, or non-recurring (see page 50 of the textbook).