Numbers are mathematical symbols which are used to represent a quantity. Integers consist of all the natural numbers, their negative values and zero. Integers cannot consist of fractional values. They only have whole number values. An integer represent the distance of a value from zero on the number line. The number to the right of zero represent positive integers and those to left of zero represent negative ones. To the right side of zero on the number line the values will keep increasing and to the left of zero on the number line the values will keep decreasing. To compare two integers, first there signs should be noticed and then there positions on number line should be considered.

## How to Compare Integers

The given symbols are used in comparing the integers.
1) ">" : This is the symbol used for greater than which is used as $a > b$ when an integer a is greater than another integer b.

2) "<" : This symbol represents less than relation. It can be used as $a<b$ when an integer a is less than integer b.
While comparing two integers the given points should be remembered.
1) When two integers a and b are given then to compare a and b, we will see which one of them is having higher distance from zero if both of       them are positive.

2)
If one is negative and other integer is positive, then the positive integer will always be higher than the negative one.

3) If both the integers are negative then the integer nearer to zero on the number line is the bigger value.

For example, the given figure shows the comparison between 5 and 3, and -5 and -3.

5 is greater than 3 whereas -5 < -3. It is so because -5 represents loss of 5 units whereas -3 represent loss of 3 units only. We can put it as,
The value of integers will keep increasing as we move on the right side of number line.

## How to Arrange Integers

A given set of integers can be arranged in two ways:
1) Ascending Order: When a collection of integers is arranged in such a way that the lower values comes at first and the higher values               comes later then it is called ascending order. It can be said that in ascending order the integers are arranged from the least value to the           highest value.

2) Descending Order: When a collection of integers are arranged in a way that the higher values come before the lower ones then it is known     as descending order. In the descending order of arrangement integers are arranged from highest value to least value.
For example, let us take a set of integers 12, 7, 15, -9, 17, -4, 5, -11.

First let us put all these numbers on a number line. The given figure shows all these integers on number line.
From the above figure we can see the number to the leftmost side which is -11. While we move towards right we find -9, -4, 7, 12, 15 and 17.

Writing in ascending order we get:
-11, -9, -4, 7, 12, 15, 17.

The descending order for the above set will be,
17, 15, 12, 7, -4, -9, -11

The descending order arrangement of a set of integers will always be reverse of the ascending order arrangement.

## Integers Word Problems

Example 1:

There are five boys Aren, Victor, David, Saif and Srikant who have obtained 89, 95, 45, 77, and 65 marks in an exam respectively. Write the names arranged in an order such that the boy getting least marks comes first and highest marks comes last.

Solution:

First we need to write all the marks in ascending order.
45, 65, 77, 89, 95

Now we will write the corresponding names in the same order.

David, Srikant, Saif, Aren, Victor
Example 2:

Four boxes A, B, C, D have weights 15, 6, 11, 9 respectively. Write the box name with highest and lowest weight.

Solution:

First we have to compare all the weights. On a number line we will represent all the weights and check.

From the above figure we find out that 6 is at the leftmost on the number line and 15 is the rightmost. Hence, taking the corresponding box names we can say that B has the lowest weight and A has the highest weight.