Inserting a Fraction between Two Given Fractions is possible. We need to follow some procedures to insert a fraction in between the other two fractions. This entire article will let you understand how to insert a fraction between two given fractions. We have given different examples to make you know about the concept of fractions on our website. Refer to 6th Grade Math to learn all the concepts required to gain the best knowledge.

Also, check:

- Numerical Expressions Involving Fractional Numbers
- Fraction of a Fraction
- Worksheet on Word Problems on Division of Mixed Fractions

## How to Insert a Fraction between Two Given Fractions?

Check out the process to know how to insert a fraction between two given fractions. The steps are given below for your reference.

- Firstly, take the given two fractions.
- Take the numerators of given fractions and add them to get a new numerator.
- Take the denominators of given fractions and add them to get a new denominator.
- Finally, place the new numerator and denominator to know the fraction that can insert in between given fractions.
- The fraction that to insert between two fractions lies between those two fractions.

Or Sum of the numerators as the new numerator or Sum of the denominators as the new denominator to get a new fraction.

**Example:** Let us take two fractions such as \(\frac { x }{ y } \) and \(\frac { m }{ n } \).

Now, add the numerators x and m which becomes {x + m} also add the denominators y and n which becomes {y + n}.

The new fraction is \(\frac { x + m }{ y + n } \).

\(\frac { x }{ y } \) < \(\frac { x + m }{ y + n } \) < \(\frac { m }{ n } \).

### Inserting a Fraction between Two Given Fractions Examples

Practice all the below examples to know how to insert a fraction in between given two fractions.

**Question 1.**

How to insert a fraction between \(\frac { 4 }{ 3 } \) and \(\frac { 5 }{ 3 } \) where \(\frac { 4 }{ 3 } \) < \(\frac { 5 }{ 3 } \).

**Solution:**

Given fractions are \(\frac { 4 }{ 3 } \) and \(\frac { 5 }{ 3 } \) where \(\frac { 4 }{ 3 } \) < \(\frac { 5 }{ 3 } \).

Now, add the numerators of the given fractions. Add 4 and 5. 4 + 5 = 9.

Now, add the denominators of the given fractions. Add 3 and 3. 3 + 3 = 6.

The new numerator is 9 and the new denominator is 6.

The fraction \(\frac { 9 }{ 6 } \) must be greater than \(\frac { 4 }{ 3 } \) and lss than \(\frac { 5 }{ 3 } \).

Therefore, \(\frac { 4 }{ 3 } \) < \(\frac { 9 }{ 6 } \) < \(\frac { 5 }{ 3 } \).

**Question 2.**

Insert a fraction between \(\frac { 10 }{ 3 } \) and \(\frac { 15 }{ 4 } \) where the inserted fraction must less than \(\frac { 15 }{ 4 } \).

**Solution:**

Given fractions are \(\frac { 10 }{ 3 } \) and \(\frac { 15 }{ 4 } \) where the inserted fraction must less than \(\frac { 15 }{ 4 } \).

Now, add the numerators of the given fractions. Add 10 and 15. 10 + 15 = 25.

Now, add the denominators of the given fractions. Add 3 and 4. 3 + 4 = 7.

The new numerator is 25 and the new denominator is 7.

The fraction \(\frac { 25 }{ 7 } \) must be greater than \(\frac { 10 }{ 3 } \) and lss than \(\frac { 15 }{ 4 } \).

Therefore, \(\frac { 25 }{ 7 } \) is less than \(\frac { 15 }{ 4 } \).

**Question 3.**

How to insert a fraction between \(\frac { 10 }{ 7 } \) and \(\frac { 3 }{ 2 } \) where the inserted fraction must greater than \(\frac { 10 }{ 7 } \).

**Solution:**

Given fractions are \(\frac { 10 }{ 7 } \) and \(\frac { 3 }{ 2 } \) where the inserted fraction must greater than \(\frac { 10 }{ 7 } \).

Now, add the numerators of the given fractions. Add 10 and 3. 10 + 3 = 13.

Now, add the denominators of the given fractions. Add 7 and 2. 7 + 2 = 9.

The new numerator is 13 and the new denominator is 9.

The fraction \(\frac { 13 }{ 9 } \) must be greater than \(\frac { 10 }{ 7 } \) and lss than \(\frac { 3 }{ 2 } \).

Therefore, \(\frac { 13 }{ 9 } \) is greater than \(\frac { 10 }{ 7 } \).

See More: Worksheet on Fractions

### FAQs on How to find a Fraction between Two Fractions

**1. What is a Fraction in math?**

A fraction is a number where it consists numerator and a denominator. In a fraction, the numerator is divided by a denominator. Also, the fraction is not a whole number.

**2. How do you Insert a Fraction between Two Given Fractions?**

To Insert a Fraction between Two Given Fractions, make a sum of the numerators and also make a sum of the denominators. Write the new numerator and denominator as a fraction to find the Inserting Fraction between Two Given Fractions.

**3. What is the Inserting Fraction between Two Given Fractions \(\frac { a }{ b } \) and \(\frac { c }{ d } \)?**

The Inserting Fraction between Two Given Fractions \(\frac { a }{ b } \) and \(\frac { c }{ d } \) is \(\frac { a + c }{ b + d } \).

**4. Insert a fraction between \(\frac { 1 }{ 2 } \) and \(\frac { 1 }{ 3 } \).**

The required fraction between \(\frac { 1 }{ 2 } \) and \(\frac { 1 }{ 3 } \) is \(\frac { 1 + 1 }{ 2 + 3 } \) = \(\frac { 2 }{ 5 } \).

**5. What is the rule to insert a fraction between two given fractions?**

The inserted fraction must lies between two given fractions i.e, if two fractions are \(\frac { a }{ b } \) and \(\frac { c }{ d } \), then \(\frac { a }{ b } \) < \(\frac { a + c }{ b + d } \) < \(\frac { c }{ d } \).

Must read the complete article and prepare yourself in a perfect way. You can easily score good marks in the exam if you follow concepts, worksheets, and practice questions available on our website.