Using ordinary positive numbers, it is not possible to work out 7 -10. Therefore the number system has to be extended to include negative numbers (numbers below zero).

The set of *positive* and *negative* whole numbers is called **integers**. That is …, -4, -3, -2, -1, 0, 1, 2, 3, 4,… and so on. Hence 7-10=-3.

To distinguish between a positive number and a negative number, we write **+3** to mean **positive 3** or simply **3** without a sign. A number without a sign is always positive. We also write **-3** to mean **negative 3**. A negative number must have a negative sign in front of it. **Zero** which is represented by the digit **0**, is *neither positive nor negative* but is included in the set of all integers.

In general, numbers that have a + or – sign in front of them are known as **directed numbers**.

**Example 1**

In a football tournament, team A scored 3 goals, while it conceded 5 goals. What aggregate number of goals did team A score?

**Solution**

The number of goals scored is considered to be positive while the number of goals conceded is taken to be negative. If the team conceded 5 goals, then it implies the team scored -5 goals. The 3 goals the team scored will reduce the aggregate number goal it conceded to 3. Hence, the aggregate number of goals scored by the team is -2, indicating that 3-5=-2.

**Example 2**

Peter’s account was in debt of GH₵5,000.00 and he deposited GH₵3,500.00 into the account. What is the balance after the deposit?

**Solution**

-5,000+3,500=-GH₵1,500.00 Hence Peter’s account is in debt of GH₵1,500.00

**SECTION 2: COMPARING AND ORDERING INTEGERS**

*The Number Line*

*The Number Line*

Every whole number can be represented by a point on a straight line called the **number line**. Numbers to the right of zero are positive numbers and those to the left of zero are negative numbers.

The number line can help you *compare* any positive and negative numbers. Any number on the line is * less than* any number on the

**of it and**

*right**any number to the*

**more than****of it.**

*left*The symbol **<** is used to mean ** less than** and the symbol

**>**is used to mean

*.*

**greater than****Example 1**

Use the inequality signs **<** or **>** to indicate the relationship among the following numbers:

**(a) -9, -6, 5, 0, 4, 3 (b) 0, 7, 2, -13, -17 (c) -4, 3, 0, 8, -10, 1**

**Solution**

**Example 2**

Use the sign **<** or **>** to make the following number statements correct.

**(a) -4 … -2 (b) -5 … 0 (c) -1 … -5 (d) -7 … -20**

**(e) -24 … -23 (f) -6 … -7 (g) -4 … 4 (h) -44 … -22**

**Solution**

**(a) -4 < -2 (b) -5 < 0 (c) -1 > -5 (d) -7 > -20**

**(e) -24 < -23 (f) -6 > -7 (g) -4 < 4 (h) -44 < -22**

##### SECTION 3: Addition of Integers

##### SECTION 4: Subtraction of Integers

##### SECTION 5: Multiplication and Division of Integers

##### SECTION 6: Properties of Integers