INTEGERS: SECTION 1: The Idea of Integers (Negative and Positive Integers)

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

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 right of it and more than any number to the left of it.

Integers from -6 to +6 represented on a number line

Integers from -6 to +6 represented on a number line

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