Addition and Subtraction of Fractions on Fraction Number Line

Different Fractions can be represented on the number line. We have explained the step-by-step procedure on how to add and subtract fractions using a number line. Refer to the solved examples on adding and subtracting fractions on the fraction number line having both same and different denominators and learn the problem-solving approach used. Students can utilize the article over here to get a deeper insight on the concept of Addition and Subtraction of Fractions on Fraction Number Line and learn them effectively.

How to Add Fractions using a Fraction Number Line?

Follow the step-by-step procedure to Add Fractions using a Fraction Number Line.

  1. Take the number line and divided it into equal parts.
  2. Divide the line into n equal parts where n is the denominator of the fraction.
  3. Take the first part of the fraction on a number line and add the second fraction to the first fraction.
  4. Then, take the last fraction as the final output of the addition of the fraction.

Examples on Addition of Fractions using a Number Line

Check out the below examples to add different fractions with the help of a number line.

Example 1.
Calculate the sum of \(\frac { 6 }{ 10 } \) + \(\frac { 3 }{ 10 } \) on the fraction number line.

Solution: 

Given fractions are \(\frac { 6 }{ 10 } \) + \(\frac { 3 }{ 10 } \)
The denominator is 10.
Take the number line and divide it into 10 equal parts.
First, take 6 parts out of 10 parts because the first fraction is \(\frac { 6 }{ 10 } \) on a number line.
Add 3 parts from the 6 out of 10 parts because the second fraction is \(\frac { 3 }{ 10 } \) on a number line.
\(\frac { 6 }{ 10 } +\frac { 3 }{ 10 } =\frac { 9 }{ 10 } \)
Finally, the final output is \(\frac { 9 }{ 10 } \).

Addition and Subtraction of Fractions on the Fraction Number Line

Example 2.
Calculate the sum of \(\frac { 2 }{ 5 } \) + \(\frac { 2 }{ 5 } \) on the fraction number line.

Solution: 

Given fractions are \(\frac { 2 }{ 5 } \) + \(\frac { 2 }{ 5 } \)
The denominator is 5.
Take the number line and divide it into 5 equal parts.
First, take 2 parts out of 5 parts because the first fraction is \(\frac { 2 }{ 5 } \) on a number line.
Add 2 parts from the 2 out of 5 parts because the second fraction is \(\frac { 2 }{ 5 } \) on a number line.
\(\frac { 2 }{ 5 } +\frac { 2 }{ 5 } =\frac { 4 }{ 5 } \)
Finally, the final output is \(\frac { 4 }{ 5 } \).

Addition and Subtraction of Fractions on the Fraction Number Line Examples

Example 3.
Calculate the sum of \(\frac { 1 }{ 7 } \) + \(\frac { 4 }{ 7 } \) on the fraction number line.

Solution: 

Given fractions are \(\frac { 1 }{ 7 } \) + \(\frac { 4 }{ 7 } \)
The denominator is 7.
Take the number line and divide it into 7 equal parts.
First, take 1 part out of 7 parts because the first fraction is \(\frac { 1 }{ 7 } \) on a number line.
Add 4 parts from the first part out of 7 parts because the second fraction is \(\frac { 4 }{ 7 } \) on a number line.
\(\frac { 1 }{ 7 } +\frac { 4 }{ 7 } =\frac { 5 }{ 7 } \)
Finally, the final output is \(\frac { 5 }{ 7 } \).

Addition and Subtraction of Fractions on the Fraction Number Line Example

How to Subtract Fractions using a Fraction Number Line?

The process of subtracting fractions using a Fraction Number Line is given below. All the steps will help you to solve the problems to subtract fractions.

  1. Take the number line and divided it into equal parts.
  2. Divide the line into n equal parts where n is the denominator of the fraction.
  3. Take the two numerator numbers on a number line.
  4. Then, subtract the small number from a large number.
  5. Finally, write the numerator and denominator to get the final answer.

Subtraction of Fractions using a Number Line Examples

Example 1.
Find the difference between \(\frac { 8 }{ 10 } \) and \(\frac { 6 }{ 10 } \)

Solution: 

Given fractions are \(\frac { 8 }{ 10 } \) – \(\frac { 6 }{ 10 } \)
The denominator is 10.
Take the number line and divide it into 10 equal parts.
Find out the numerators on a number line 8 and 6.
Subtract 6 from the 8 on a number line. Then, you will get 2.
So, \(\frac { 8 }{ 10 } – \frac { 6 }{ 10 } =\frac { 2 }{ 10 } \)
The remaining part on the number line after subtraction is \(\frac { 2 }{ 10 } \).
Finally, the final output is \(\frac { 2 }{ 10 } \).

Addition and Subtraction of Fractions on the Fraction Number Line Solved Example

Example 2.
Find the difference between \(\frac { 4 }{ 5 } \) and \(\frac { 1 }{ 5 } \)

Solution: 

Given fractions are \(\frac { 4 }{ 5 } \) – \(\frac { 1 }{ 5 } \)
The denominator is 10.
Take the number line and divide it into 5 equal parts.
Find out the numerators on a number line 4 and 1.
Subtract 1 from the 4 on a number line. Then, you will get 4 – 1 = 3.
So, \(\frac { 4 }{ 5 } – \frac { 1 }{ 5 } =\frac { 3 }{ 5 } \)
The remaining part on the number line after subtraction is \(\frac { 3 }{ 5 } \).
Finally, the final output is \(\frac { 3 }{ 5 } \).

Addition and Subtraction of Fractions on the Fraction Number Line Solved Examples

Example 3.
Find the difference between \(\frac { 5 }{ 7 } \) and \(\frac { 2 }{ 7 } \)

Solution: 

Given fractions are \(\frac { 5 }{ 7 } \) – \(\frac { 2 }{ 7 } \)
The denominator is 7.
Take the number line and divide it into 7 equal parts.
Find out the numerators on a number line 5 and 2.
Subtract 2 from the 5 on a number line. Then, you will get 5 – 2 = 3.
So, \(\frac { 5 }{ 7 } – \frac { 2 }{ 7 } =\frac { 3 }{ 7 } \)
The remaining part on the number line after subtraction is \(\frac { 3 }{ 7 } \).
Finally, the final output is \(\frac { 3 }{ 7 } \).

Addition and Subtraction of Fractions on the Fraction Number Line Solved problems

FAQs on Adding and Subtracting Fractions on the Fraction Number Line

1. How do you represent a fraction on a number line? Give Example?

For example \(\frac { 3 }{ 5 } \) is the fraction, we can take it on a number line by dividing the number line into 5 parts and at third part it is represents as \(\frac { 3 }{ 5 } \).

2. Can I add or subtract fractions using a number line?

Yes, it is easier to represent the addition or subtractions of fractions using a number line.

3. What does \(\frac { 4 }{ 5 } \) mean?

\(\frac { 4 }{ 5 } \) means 4 out of 5 parts.

4. Can I add or subtract unlike fractions using a number line?

Yes, you can add or subtract unlike fractions using a number line.

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