Number Line

The first question that comes to our mind is – what is a number line? The number line is nothing but a simple representation of numbers on a horizontal straight line. More precisely, the number line consists of both positive and negative integers. The line consists of numbers placed at equal intervals and can be extended indefinitely on both the negative and positive sides. An example of a number line is

The importance of a number line is that students generally use it to visualise numbers on a line for easy addition and subtraction of the numbers.

History

John Wallis first mentioned the concept of the Number line in his Treatise of Algebra. According to him, the addition and subtraction on the number line are easily done by moving forward or backwards.

What is a Number line?

• In simple words, the number line is nothing but a horizontal line with numbers marked on it at regular intervals

• The numbers plotted on the number line can be positive or negative whole numbers, fractions, or decimals

• The way of representing numbers on a number line makes it easy to visualise numbers and perform mathematical calculations 

• The number line is known to consist of both negative and positive numbers

• The negative numbers are always placed on the left-hand side to that of 0, and the positive numbers are always placed on the right-hand side of the 0 on the number line 

• In the number line, the numbers are present in increasing order from left to right. For e.g. (-6) being smaller than (-5) is placed on the left side of (-5). It is also considered that 0 is the origin of the number line

•  It is also interesting to know that decimals can also be plotted on the number line with proper intervals and markings

Mechanism of Drawing a Number Line

The number line can be drawn in 4 easy steps;

• Step 1- a horizontal line is drawn with arrows on both sides, indicating that the lines are non-ending and increase up to infinity on both sides

• Step 2- a proper scale is chosen for drawing the number line. If a number like 50 or 20 needs to be plotted on a number line, then a scale of multiple of 5 can help plot the number

• Step 3- the most important step is to make sure that the points are marked at equal intervals

• Step 4- the last step is to locate the desired number on the number line and then highlight or circle it for reference

Examples of Number Line

A number line can be used to represent integers, real numbers, whole numbers, or even decimals. An example of a number line is

Importance and Application of Number line

There are multiple applications of a number line:

• It is used by children during their school curriculum to enhance their skills of tackling numbers easily

• The numbers placed on the number line can be compared with each other to determine the greater and smaller number among the two

• The representation of numbers on the number can be used to easily add or subtract numbers

Adding Numbers on the Number Line

Both positive and negative integers can be added to specific numbers on a number line. 

• Let us consider the positive number 2. If we have to add the positive number 4 to the number 2, we will move four places towards the right on the number line from the number 2. This will lead us to the final number 6 on the number line. This is how it can be calculated on the number line

• Now let us consider 2 negative integers that need to be added, like -3 and -4. We start from the number -3 on the number line, and we move 4 places towards the left side of the number line and end up at the number -7 

Subtracting Numbers on the Number Line

• We move towards the left on the number line to subtract positive integers. For example, if we have to subtract 3 from 5 then we will move 3 places towards the left from the number 5 on the number line leading us to the number 2. We know that 5 – 3= 2

• For negative integers, we move towards the right on the number line. Let us consider two negative integers -5 and -3. If we want to subtract -5 from -3 we will first track -3 on the number line and then move 5 places towards the right, which will lead us to the number 2. We know (-3) – (-5) = 2

Conclusion

Numbers play a very important role in our daily life to count, measure, or label objects and they can be easily represented on a horizontal line – this line is a number line. Children use the number line to learn addition and subtraction easily. The number line consists of both positive and negative integers. There is a different process for the addition of positive and negative integers on a number line. The importance of a number line is to help in addition, subtraction, and comparison between integers and numbers.