Comparison of Integers

We know that on a number line the number on the right is always greater than the number on the left. Same applies for integers also. -1 > -2, -2 > -3 and so on.

$Integers on Number Line$

From the above number line we can say that 0 separates the positive and negative integers. 0 is on the left of all the positive integers. So, 0 is less than every positive integer. 0 is on the right of all the negative integers. So, 0 is greater than every negative integer. All the positive integers are greater than negative integers.

Comparison of integers: When we represent integers on the number line, we observe that the value of the number increases as we move towards right and decreases as we move towards left.

$Comparison of Integers$

1 < 2 < 3 …..

-1 > -2 > ……

The whole numbers are on the right side of the 0 and in the left side of the 0 there are negative numbers.

Note:

(i) Zero is less than every positive integer, and greater than every negative integer. Zero is neither positive nor negative.

For example, 0 < 1, 0 < 10, etc.

Also 0 > -1, 0 > -5, etc.

(ii) Every positive integer is greater than every negative integer.

For example, 2 > -2, 2 > -1, 1 > -1 etc.

(iii) There is no greatest or smallest integer.

(iv) The smallest positive integer is 1 and the greatest negative integer is -1.

Solved Examples on Comparison of Integers:

1. Which is greater +1 or -6?

Solution:

Since +1 lies to the right of 0 on the number line. +1 is greater than -6.

2. Which is greater -27 or -34?

Solution:

-34 is 34 units away to the left of 0. -27 is 27 units away to the left of 0. So, -27 is to the right of -34. -27 > -34.

3. Arrange +27, -32, +16 and -12 in ascending order.

Solution:

Let us mark the integers on the number line.

$Comparison of Integers$

Thus, the integers in ascending order are -33, -15, +18, +29

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