# Rational Numbers between Two Rational Numbers

0
39

A Rational Number is a number that can be expressed in the form of p/q where q ≠ 0. If you want help in inserting  Rational Numbers between Two Rational Numbers make use of this article. Check out the Step by Step Process to find the Rational Numbers between Two Rational Numbers of either Same or Different Denominator. Have a glance at the solved examples and understand the concept better.

We can insert infinitely many rational numbers between Two Rational Numbers. This Property of Rational Numbers is called Dense Property.

### How to find Rational Numbers between Two Rational Numbers with the Same Denominator?

• The first and foremost step while finding the Rational Numbers between Two Rational Numbers is to check the values of Denominators.
• In the case of the same denominators check the value of the numerator.
• If the numerators differ by a large value then you can simply write the rational numbers with an increment of one while keeping the denominator part unaltered.
• If the numerators differ by a smaller value than the number of rational numbers to be found simply multiply the numerators and denominators by multiples of 10.

Examples

Find 4 Rational Numbers between 1/8 and 6/8?

Solution:

Since the Denominators of Two Rational Numbers are Same and Numerators differ by a large value increment the numerator by 1 while keeping the Denominator Unaltered.

2/8, 3/8, 4/8, 5/8 are the 4 Rational Numbers that lie between 1/8 and 6/8.

Find 10 Rational Numbers are to be found between 1/5, 4/5?

Solution:

If 10 Rational Numbers are to be found between 1/5, 4/5 both the rational numbers are to be multiplied by 10.

1/5*10/10 = 10/50

4/5*10/10 = 40/50

10 Rational Numbers between 10/50 and 40/50 are 11/50, 12/50, 13/50, 14/50, 15/50, 16/50, 17/50, 18/50, 19/50, 20/50.

### How to find Rational Numbers between Two Rational Numbers with the Different Denominators?

• To find Rational Numbers between Two Rational Numbers with the Different Denominators you need to equate the Denominators firstly.
• You can Equate the Denominators by finding their LCM or by multiplying the denominators of one to another one’s numerator and denominator.

Example

1. Find Rational Numbers between 1/2 and 3/4?(At least 5)

Solution:

Since the Rational Numbers given doesn’t have the same denominator firstly equate the denominators.

Equating the Rational Numbers we have

1/2*4/4 = 4/8

3/4*2/2 = 6/8

We can’t write 5 Rational Numbers between 6/8 and 4/8. Multiply the Numerators and Denominators by multiples of 10.

4/8*10/10 = 40/80

6/8*10/10 = 60/80

5 Rational Numbers between 40/80 and 60/80 are 41/80, 42/80, 43/80, 44/80, 45/80.