Subtraction on Number Line: The number line is a horizontal line extending infinitely to either side in which the numbers are placed in equal intervals. It is the visual representation of numbers on a straight horizontal line. Zero is marked at the middle of the number line, positive numbers are placed to the right of the zero, and negative numbers to the left side of zero.

To subtract the numbers, we will move to the left side of the number line. It is also important to note that while subtracting two fractions, the denominators of both the fractions should be the same. If the denominators are different then we have to use similar fractions with the same denominator. In this article, we will learn about the subtraction on the number line in detail.

What is a Number Line?

A number line is a straight line with the numbers marked at equal intervals along its length. A number line can be extended infinitely in any direction and represented horizontally. A number line is the backing for comparing and ordering numbers. The number line is a way to describe any real number that includes every whole number and natural number.

Representation of Numbers on Number Line

We can explain all arithmetic operations such as the addition, subtraction, multiplication, and division of numbers on the number line. But first, you must understand how to locate the numbers on the number line. The number zero is placed in the middle of a number line, and all positive numbers are on the right side of the zero, whereas negative numbers are on the left side of zero. In other words, if we move to the left side of zero, the value of the number decreases, and if we move to the right side of zero, the value of the number increases.

Subtraction

Subtraction means taking out the difference between two numbers. The term is represented as \(“-“.\)

Example: To find the difference between \(29\) and \(19\) so you write it as \(29-19=10.\)

Subtraction on a Number Line

As discussed above, the number line is the visual representation of numbers on a straight horizontal line. 

The numbers on the number line are shown below, with zero in the middle, positive numbers to the right side of the zero and negative numbers to the left side of the zero.

The subtraction on the number line is the way to find the difference between two numbers on the horizontal line with the numbers placed at equal intervals.

The two steps to be followed to find subtraction on a number line are:

1. Move left when subtracting the positive integers.
2. Move towards the right side of the zero to subtract the negative integers.

Subtraction of Positive Numbers

When you want to subtract two positive numbers, move on to the left as far as the value of the second number.

Example: Subtract \(5\) from \(4\)

Here the first number is \(4,\) and the second number is \(5\); both are positive. First, mark the number \(4\) on a number line and then move \(5\) steps to the left. It will give \(-1\) as a result.

Subtraction of Negative Numbers

When you want to subtract two negative numbers, then move towards the right side as far as the value of the second number.

Example: Subtract \(-4\) from \(-2\)

First, locate \(-2\) on the number line and move \(4\) steps to the right to reach \(2.\)

Representation of Fractions on Number Line

The term used to represent the part of the whole is called a fraction. There are two parts in a fraction, namely, numerator and denominator.

Fractions can be classified as:
1. Proper Fractions
2. Improper Fractions
3. Mixed Fractions

We know how to represent numbers on the number line. Now, let us try to represent fractions, for example \(\frac{1}{2}\) on a number line. It is clear that \(\frac{1}{2}\) is greater than the number \(0\) and less than the number \(1.\)

So, it must lie in between \(0\) and \(1.\) Since the denominator of the given fraction is \(2,\) divide the space between \(1\) and \(2\) into two equal parts.

Subtraction of Fractions on Number Line

While subtracting two fractions, the denominators of both the fractions should be the same. If you have different denominators, then you have to use equivalent fractions with the same denominator. You have to take out the least common multiple (LCM) of the two denominators in this case. To subtract the given fractions with unlike denominators, write the fractions with a common denominator. Then, simplify.

For example, if we need to subtract \(\frac{5}{{10}} – \frac{3}{{10}}\), first, make ten equal spaces between \(0\) and \(1.\) Then mark \(\frac{5}{10}\) on a number line, and jump \(3\) steps left to \(\frac{5}{10}\) to get the required answer.

From the above number line, \(\frac{5}{{10}} – \frac{3}{{10}} = \frac{2}{{10}}\)

Let us understand subtraction on number line facts through some solved examples.

Solved Examples on Subtraction on Number Line

Q.1. Subtract the fractions \(\frac{5}{{10}} – \frac{4}{{10}}\) on the number line.
Ans: We need to subtract \(\frac{5}{{10}} – \frac{4}{{10}}\) , first, make ten equal space between \(0\) and \(1\). Then mark \(\frac{5}{10}\) on a number line, and jump \(4\) steps left to \(\frac{1}{10}\) to get the required answer.

Hence, the required answer is \(\frac{5}{{10}} – \frac{4}{{10}} = \frac{1}{{10}}\)

Q.2. Subtract the numbers \(4\) from \(8\) using the number line.
Ans: Given, \(8-4\)
First, mark the number \(8\) on the number line and then take the jumps of \(4\) by counting backwards until you reach \(4\).

Hence, the required answer is \(8-4=4\)

Q.3. Subtract the fractions \(\frac{9}{8} – \frac{6}{8}\) on the number line.
Ans: Given, \(\frac{9}{8} – \frac{6}{8}\)
To subtract the fractions, starting from \(\frac{9}{8}\) we will take \(6\) jumps from there to reach \(\frac{3}{8}.\)

Hence, the required answer is \(\frac{9}{8} – \frac{6}{8} = \frac{3}{8}\)

Q.4. Subtract the numbers \(3\) from \(7\) using the number line.
Ans: Given, \(7-3\)
First, mark the number \(7\) and then take the jumps of \(3\) to the left side by counting backwards until you reach \(4\).

Hence, the required answer is \(7-3=4.\)

Q.5. Subtract \((-6)-(-2)\) on the number line.
Ans: First, mark the given number \(-6\) on the number line.

Now, take \(2\) steps from \(-6\) on the positive side of the number line to reach \(-4.\)
Hence, the required answer is \(\left( { – 6} \right) – \left( { – 2} \right) = \, – 4.\)

Summary

A number line is described as a straight line with the numbers marked at equal intervals along its length. The number line is a way to represent any real number that involves whole numbers and natural numbers. Subtraction is defined as taking out the difference between two numbers.

In this article, we discussed the definition of the number line and how to represent the numbers on the number line. We understood the concept with subtraction on the number line example. Finally, we studied the representation of fractions on the number line covering subtraction of fractions on the number line.

FAQs on Subtraction on Number Line

Q.1. Explain Subtraction on Number Line with an example?
Ans: When you want to subtract two numbers on the number line, move to the left as far as the value of the second number.
Example: Subtract \(5\) from \(4\)
Here the first number is \(4,\) and the second number is \(5\); both are positive. First, mark the number \(4\) on a number line and move \(5\) steps to the left to get the answer as \(-1.\)

Q.2. How do you subtract fractions from a whole number on a number line?
Ans: We will deduct a mixed fraction from the whole number to understand this. For the process, follow the given steps:
a. First, you have to subtract the whole numbers on the number line. Consider the subtraction of numbers \(5 – 4\frac{2}{3}.\)
b. Subtract the whole numbers on the number line; in our case, it is \(5-4=1.\)
c. Note that the denominators of the fraction should be the same.
d. The fraction you have is \(\frac{2}{3}\) on the number line.
e. Take two jumps from the whole number \(1\) you got by subtracting the whole numbers to the left side.
f. You will reach the fraction \(\frac{1}{3}.\)
g. Thus the answer you got after subtracting \(5 – 4\frac{2}{3} = 1\frac{1}{3}.\)
h. You can cross-verify the answer by adding the fraction \(1\frac{1}{3}\) with the fraction you have in the question, \(1\frac{1}{3} + 4\frac{2}{3}\) you get the whole number \(5\) as the answer.
i. Hence your answer is correct.

Q.3. How do you do subtraction on a number line?
Ans: When you want to do subtraction using a number line, you have to count by moving one number at a time towards the left side from the number zero.

Q.4. How do you subtract \(3\) digit numbers on a number line?
Ans: Let us understand this by subtracting \(232-137\) on the number line. First, draw a horizontal line and count from the number \(0\) to \(232.\) Next, count \(137\) from \(232\) in reverse order. Finally, you get the answer as \(232-137=95.\)

Q.5. How do you borrow numbers when subtracting?
Ans: For using the borrow method in subtraction, follow the steps given below: 
a. Subtract one from the maximum number in the column directly to the left.
b. Then cross out the number you are borrowing from,  subtract one and write the answer above the number you have crossed out.
c. Finally, add \(10\) to the maximum number in the column that you were working on.

Some other helpful articles by Embibe are provided below:

Class-wise Mathematical Formulas

Maths Formulas For Class 6

Maths Formulas For Class 7

Maths Formulas For Class 8

Maths Formulas For Class 9

Maths Formulas For Class 10

Maths Formulas For Class 11

Maths Formulas For Class 12

We hope this article on subtraction on the number lines has provided significant value to your knowledge. If you have any queries or suggestions, feel to write them down in the comment section below. We will love to hear from you. Embibe wishes you all the best of luck!