Rational Numbers are the numbers that can be denoted in the form of fraction p/q where p, q are integers and q is a non-zero number. In this article, we will discuss how to find rational numbers between two unequal rational numbers explained in detail. Know the formula for finding rational numbers between two unequal rational numbers, solved examples on finding rational numbers between given two unequal rational numbers mentioned step by step.
How to find Rational Numbers between Two Unequal Rational Numbers?
Go through the below process and learn how to find rational numbers between two unequal rational numbers. They are as under
Let us consider a and b are two unequal rational numbers if we are to find the rational number preset between them we can find so by using the formula (a+b)/2. Rational Numbers are Ordered i.e. given two rational numbers a, b either a >b, a<b, a=b.
We can also say there is an infinite number of rational numbers between two unequal rational numbers.
How to find Rational Numbers between Two Unequal Rational Numbers having Same Denominator?
- Firstly, check the denominators of the given rational numbers.
- For fractions having the same denominators check for the numerators.
- If the numerators differ by a larger value then we can write the rational numbers with increments of one for numerator without changing the value of the denominator.
- If the numerators differ by a lesser value then multiply both the numerators and denominators of rational numbers by multiples of 10.
How to find Rational Numbers between Two Unequal Rational Numbers having Different Denominator?
- In order to find the rational numbers between two unequal rational numbers having different denominators, equate the denominators.
- Equate the denominators using the LCM Method.
- After applying the LCM Method and making the denominators equal apply the rules for finding rational numbers between two unequal rational numbers of the same denominators.
Also, See:
- Comparison between Two Rational Numbers
- Recurring Decimals as Rational Numbers
- Laws of Algebra for Rational Numbers
Solved Examples on How to find a Rational Number Between Two Fractions
Example 1.
Find a Rational Number lying mid-way between 4/3 and 6/7?
Solution:
Given rational numbers are 4/3 and 6/7
We know the formula to find rational number lying midway = (a+b)/2
=(4/3+6/7)/2
=((28+18)/21/2)
=(46*/21)/2
=46/42
Example 2.
Find a rational number lying mid-way between 7/5 and -13/2?
Solution:
Given rational numbers are 7/5 and -13/2
We know the formula to find rational number lying midway = (a+b)/2
=1/2(7/5+-13/2)
=1/2(14-65/10)
=1/2(-51)
=-51/2
Example 3.
Find 5 rational numbers between 3/4 and -7/4?
Solution:
Given rational numbers are 3/4 and -7/4
Here rational numbers are having the same denominators. However, the difference between them is less we will multiply both numerators and denominators with 10.
3/4 = 3*10/4*10 = 30/40
-7/4 = -7*10/4*10 = -70/40
Integers between -70 & 30 are -70<-69<-68<-67<-65<……….28<29<30
Therefore, the 5 rational numbers between 3/4 and -7/4 are -69/40, -68/40, -67/40, -66/40, -65/40.
Example 4.
Find at least 10 Rational Numbers between fractions 1/2 and 5/4?
Solution:
Given rational numbers are 1/2 and 5/4
Here rational numbers are having different denominators. So we will equate the denominators using LCM Method. Doing so we will obtain the fractions as under
LCM(2,4) = 4
1/2 = 1*2/2*2 = 2/4
5/4 =5*1/4*1 = 5/4
Now that we have made Denominators the Same by equating let us apply the further process same as in the process of finding the rational numbers between two unequal rational numbers of same denominators
However, the difference between them is less we will multiply both numerators and denominators with 10.
2/4 = 2*10/4*10 = 20/40
5/4 = 5*10/4*10 = 50/40
Integers between 20 & 50 are 21< 22<23<24<25<26<27…….46<47<48<49<50
Therefore, the 10 rational numbers between 1/2 and 5/4 are 21/40, 22/40, 23/40, 24/40, 25/40, 26/40,27/40,28/40, 29/40,30/40.