comparing numbers

Comparing numbers in mathematics is when you determine if one number is smaller, bigger than, or equal to another number. In Mathematics we use symbols to show this comparison between two numbers: the equal (=), less than (<), and greater than (>) signs. The scope of this lesson is limited to integers. 

We are going to learn:

• Why do we need to compare numbers? 
• How to use a number line?
• How to compare two natural numbers? 
• How to compare two integers? 

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  If Mary has 7 apples and Suzy has 5 apples, we would like to know who has more apples.

Mary
Suzy

Here looking at the picture we can visually compare and see that it looks like Mary has more apples. But every time this is not possible. When we don't have a picture to look at, we can compare the numbers.

Let us learn how to compare numbers. There are two ways to compare numbers:

• Count: The number you get first in counting is smaller. 5 comes before 7, therefore 5 is smaller than 7.
• Compare using a number line.  
   

Using a Number Line:

The easiest way to learn comparing numbers is by using a Number Line. The number line can be defined as a straight line with numbers placed at equal intervals along its length. On a number line, the positive numbers are to the right of zero and the negative numbers are to the left of zero. Negative numbers are any number to the left of zero on the number line. They are represented by the − sign attached on the left of the number. 

Writing numbers on a number line make comparing numbers easier. The numbers on the left are smaller than the numbers on the right of the number line.
 

Comparing Natural Numbers:

• Natural numbers are positive whole numbers, sometimes including the number zero. To show how to compare two natural numbers we will pick one number from the above number line. If we pick the number 2, we can say that the numbers which are on the right of number 2 are greater, and the numbers which are on the left of number 2 are smaller. For example, number 8 is positioned to the right of number 2, therefore 8 is greater than 2. 1 is positioned to the left of 2, and therefore 1 is lesser than 2.

We can use signs to express a comparison between numbers. They are:

Sign	Meaning	Examples
=	When two values are equal	3=3 2=2
<	When one value is smaller than the other	3 < 5 5 < 6
>	When one value is bigger than another	4 > 2 6 > 5

Remember that the tip of the arrow is always on the side of the smaller number and a wide part of the arrow is always on the side of the larger number.

    BIG > small

OR

    small < BIG
 

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Comparing Integers (both positive and negative whole numbers):

Let us again use the number line to compare integers.

• The value of negative numbers is always less than the value of positive numbers. For example,
  -3 < 2
  -3 < 0
  -3 < 3
   
• For integers also the same condition holds true, i.e. number which is on the right of the number is greater and the number which is on the left of the other number is lesser.  For example,
  -7 < -3
  -2 < 0
  -1 < 1

Ascending and Descending Order:
Numbers are said to be in ascending order when numbers are arranged from the smallest to the largest number. For example, 2, 9, 11, 13, and 30 are arranged in ascending order. Numbers are said to be in descending order when numbers are arranged from the largest to the smallest number. For example, 30, 13, 11, 9, and 2 are arranged in descending order.