# Comparing integers

## How to compare integers?

In this chapter we will learn two methods to compare integers.

(a) Comparing Integers – Simple Method
(b) Integer comparison using Number line.

### Comparing Integers – Simple Method

In this method there are three possible scenarios;

(i) Both integers are positive
(ii) One integer is positive and other is negative.
(iii) Both integers are negative

Let’s discuss each scenarios in detail.

#### (i) Both integers are positive

When we have positive integers, the one with the higher value is greater.

Example 01
Compare 21 and 36

Both integers are positive.
Here number 36 is the greater integer.

Example 02
Compare 99 and 101

Both integers are positive.
Here number 101 is greater integer.

#### (ii) One integer is positive and other is negative

In this case, the positive integer is greater.

When positive and negative number is given, there is no need to check the values as the positive number will always be greater.

Example 01
Compare -8 and 1

Negative Number = -8
Positive number = 1

Number 1 is greater among the two.

Example 02
Compare -99 and 80

Negative Number = -99
Positive Number = 80

Number 80 is greater among the two.

#### (iii) Both Integers are negative

When both the numbers are negative integers then the integer with smaller number is greater.

When negative numbers are given we have to look for number which is closer to 0 in number line.

The negative number closest to 0 will be the greatest.

Example 01
Compare -8 and -6

Here both the integers are negative.
Here 6 is smaller number than 8.

So -6 is closest to 0 than -8.
Hence., -6 is greater.

Example 02
Compare -3 and -4

Both the given numbers are negative integers.
Here number 3 is smaller than 4.

So -3 is greater than 4 as it lies closer to zero in number line.

I hope the concept is clear, let us now learn to compare integers using number line.

### Integer comparison using number line

When two or more integers are given then the number which lies on the right is the greatest integer.

In number line, there are three sets of numbers, positive numbers, zero and negative numbers.

You have to locate the numbers on number line and find the one located at extreme right because it will be the greatest integer.

Example 01
Which number is greater -5 or 2?

Given below are the numbers on number line.

You can see that number 2 is located on right side of number line.

Hence integer 2 is greater than -5

Example 02
Which integer is greater 3 or 6?

Number 6 is located on right side of number line.

Hence, integer 6 is greater than 3.

Example 03
Which integer is greater -3 or -7.

-3 is located on right side of number line.

Hence, integer -3 is greater than -7.

## Comparing Integers – Solved Examples

(01) Solve and find the greater number.
(a) -17 or 17
(b) -3 or 0
(c) -5 or 3
(d) 5 or 8
(e) -3 or -2

Solution

(a) -17 or 17

Among the positive and negative integers, the positive number is always the greatest.

Number 17 is the greater number.

(b) -3 or 0

On the number line number 0 lies on the right side.
Hence, number 0 is greater.

(c) -5 or 3

Between positive and negative integer, the positive number is always the greatest.

Number 3 is larger among the two.

(d) 5 or 8

Here both positive numbers are given.
We know that 8 > 2.
Hence, number 8 is larger.

(e) -3 or -2

Here both the given numbers are negative.

On comparing negative numbers, the one with smaller value is the greatest.

We know that 2 is the smaller value as 2 < 3

So, -2 > – 3
Hence, -2 is greater than -3.

(02) Arrange the following number in ascending order ( from smallest to greatest)

(i) 25, 15, 30
(ii) 10, -6, 2
(iii) -8, 0, -11
(iv) -1, -7, -5

Solution

(i) 25, 15, 30

All the given numbers are positive, so arrange the numbers from smallest value to largest value.

15 < 25 < 30

(ii) 10, -6, 2

The given numbers are collection of positive and negative numbers.

-6 ⟹ smallest number as it is negative.

Comparing 10 and 2.
We know that 10 > 2.

Arranging the numbers in ascending order.
-6 < 2 < 10

(iii) -8, 0, -11

Marking the above numbers in number line

Among the given numbers, 0 appears first on the right side then -8 and then -11.

So 0 is the greatest and -11 is the smallest.

Arranging numbers from smallest to greatest;
-11 < -8 < 0

(iv) -1, -7, -5

All the given numbers are negative integers.

The number farthest from 0 is the smallest.

-1 ⟹ 1 unit left from 0
-7 ⟹ 7 unit left from 0
-5 ⟹ 5 unit left from 0

-7 is the farthest from 0 so it is the smallest integer.
-1 is nearest from 0 hence it is greatest number

Arranging the numbers in ascending order;
-7 < -5 < -1