Explain the concept of integers

A number line is a straight line with equally spaced points that helps us see how integers are arranged.

• Zero (0) is the middle point, separating positive and negative integers.
• Positive integers are to the right of zero: 1, 2, 3, 4, ... (these can be written with or without the + sign)
• Negative integers are to the left of zero: −1, −2, −3, −4, ...

$\text{←--- negative integers ---} \; \boxed{-4} \; \boxed{-3} \; \boxed{-2} \; \boxed{-1} \; \boxed{0} \; \boxed{1} \; \boxed{2} \; \boxed{3} \; \boxed{4} \; \text{--- positive integers ---→}$

Positive integers are all numbers greater than zero. They are written as 1, 2, 3, 4, and so on. When we write them on a number line, they appear to the right of zero. We can also write them with a plus sign, such as +1, +2, +3, but the plus sign is usually optional.

Negative integers are all numbers less than zero. They are written with a minus sign in front, such as −1, −2, −3, −4, and so on. On a number line, they appear to the left of zero.

Zero is a special integer. It is neither positive nor negative. It acts as the dividing line between positive and negative integers on the number line.

Every positive integer has an opposite negative integer, and vice versa. The opposite of a number is the same distance from zero but on the opposite side of the number line.

• The opposite of +5 is −5
• The opposite of −7 is +7 (or simply 7)
• The opposite of 12 is −12
• The opposite of −3 is 3

Worked Example

Write the opposite of each integer:

(a) +8
(b) −15
(c) 23
(d) −40

Answers

(a) The opposite of +8 is −8
(b) The opposite of −15 is 15
(c) The opposite of 23 is −23
(d) The opposite of −40 is 40

In Tanzania, we use integers in many everyday situations. For example, when checking the temperature in Dodoma or Dar es Salaam, a temperature of 15°C above zero is written as +15°C, while a temperature of 8°C below zero is written as −8°C. Also, when accounting for money received and money spent, profit can be shown as a positive integer and loss as a negative integer.