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Integers

We use mathematical symbols such as > (Greater than), < (Less than), and = (Equal to) to make a comparison between two numbers.

How will we compare two numbers with the help of a number line?

We use this concept to compare between integers and put the symbols (>, <, and =) accordingly.

If we compare between –8 and –2 with the help of number line, then we will find that –8 is to the left of –2. Hence, we can write –8 < –2.

Sometimes it is difficult to locate large integers such as 5093, 805, etc. and small integers such as –596, –8053, etc. on a number line. In such cases, we cannot compare the integers using number line. We will solve the problem by keeping some facts in our mind. They are as follows.

  1. All positive integers are greater than 0 and the negative numbers. For example, 20 > 0 and 30 > –3.

  1. 0 is always greater than negative integers. For example, 0 > –5.

  1. To compare two negative integers, we first neglect the negative sign and then if the integer without negative sign is greater than the other integer, then that negative integer is smaller than the other negative integer.

For example, if we compare between –112 and –535, then first of all we have to neglect the negative sign of both the numbers. After neglecting the negative sign, the numbers are 112 and 535. Here, 535 > 112. Hence, –535 < –112

So far we have learnt the comparison of two integers. Now, let us discuss ordering of more than two integers. For ordering of integers, we use the concept of comparison of integers. It can be explained with the help of the given video.

Let us discuss some examples based on comparison and ordering of integers.

Example 1:

Fill in the boxes with appropriate signs (> or < or =) using a number line.

(a)

(b)

(c)

(d)

(e)

(f)

Solution:

Let us draw a number line as follows.

(a) On comparing –5 and 8 on the number line, we observe that –5 is to the left of 8.

Therefore,

(b) On comparing –3 and –7 on the number line, we observe that –3 is to the right of –7.

Therefore,

(c) On comparing –8 and –4 on the number line, we observe that –8 is to the left of

4.

Therefore,

(d) Oncomparing 2 and –9 on the number line, we observe that 2 is to the right of –9.

Therefore,

(e) Oncomparing –3 and 0 on the number line, we observe that –3 is to the left of 0.

Therefore,

(f) –6 is equal to –6 itself. It is neither greater nor smaller than itself.

Therefore,

Example 2:

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