In ordering integers we will learn how to order the integers on a number line.
An integer on a number line is always greater than every integer on its left. Thus, 3 is greater than 2, 2 > 1, 1 > 0, 0 > -1, -1 > -2 and so on.
Similarly, an integer on a number line is always lesser than every integer on its right. Thus, -3 is less than -2, -2 < -1, -1 < 0, 0 < 1, 1 < 2 and so on.
(i) Every positive integer is greater than every negative integer.
(ii) Zero is less than every positive integer and is greater than every negative integer.
(iii) The greater the number, the lesser is its opposite.
i.e., 8 is greater than 5, but -8 is less than -5; similarly, -9 > -15 or, 9 < 15 and so on
(iv) The lesser the number, the greater is its opposite.
i.e., 6 is less than 7, but -6 is greater than -7; similarly, -8 < -5 or 8 > 5 and so on.
Note: The symbol (-) is used to denote a negative integer as well as for subtraction.
(i) The temperature at an Everest is -10°C. Here the symbol (-) indicates the negative integer (-10) and no subtraction is involved.
(ii) On the other hand, 23 – 7 indicates the subtraction of 7 from 23.
Solved examples on ordering integers:
1. Arrange the integers from greater to lesser:
(i) 9, -2, 3, 0, -5, -7, 7, -1
(ii) -11, 17, -2, 2, -6, -15, 0, 1
(iii) 12, -21, -18, 14, -5, -1, 1, 10
Solution:
(i) 9, 7, 3, 0, -1, -2, -5, -7
(ii) 17, 2, 1, 0, -2, -6, -11, -15
(iii) 14, 12, 10, 1, -1, -5, -18, -21
2. Arrange the integers from lesser to greater:
(i) 0, 4, -4, 9, -10, -7, 12, -13
(ii) -14, 7, -25, -17, 20, 5, -9, -3
(iii) -6, 4, -18, 21, 29, -8, -16, 19
Solution:
(i) -13, -10, -7, -4, 0, 4, 9, 12
(ii) -25, -17, -14, -9, -3, 5, 7, 20
(iii) -18, -16, -8, -6, 4, 19, 21, 29
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