This document provides solutions to two problems about finding rational numbers between given values. For the first problem, it finds the three rational numbers between 1 and 2 using an average method and a number line method. For the second problem, it finds the three rational numbers between 1/3 and 7/2 again using an average method and a method of converting the fractions to a common denominator. The document explains each step of the solutions in detail.

1. Number System
Problems
Tutorial on Rational Number’s
Class 9

2. Problems on Rational Numbers
Problem 1
Find the 3 rational number between 1 and 2
Solution
Method 1 Average method
We know the average of two rational number lies between
them and it is a rational number
Step 1: First average =
1+2
2
=
3
2
So 3/2 lies between 1 and 2
Step 2: Average of 1 and 3/2 will also lie between 1 and 3/2
and hence 1 and 2,
So =
1
2
1 +
3
2
=
5
4
Step 3.: Again Average of 3/2 and 2 will also lie between 1
and 2. So
1
2
3
2
+ 2 =
7
4

3. Continued
• Method 2: Another simple way would be
from Number line
So we knows 2.1,2.2,2.3 lies between 2 and 3
Since they are terminating decimal, they are
rational numbers

4. Problems on Rational Numbers
Problem 2
Find the 3 rational number between 1/3 and 7/2
Solution
Method 1 Average method
We know the average of two rational number lies between
them and it is a rational number
So step 1: First average =(1/3+7/2)/2=23/24
So 23/24 lies between 1/3 and 7/2
Step 2: Average of 1/3 and 23/24 will also lie between 1/3 and
23/24 and hence 1/3 and 7/2
So = ½(1/3+23/24)=31/48
Step 3.: Again Average of 23/24 and 7/2 will also lie between
1/3 and 7/2. So=1/2(23/24+7/2)=107/48

5. Continued
• Method 2: Another simple way would be to
convert the denominator into same value
1/3 =2/6
7/2=21/6
Now 2/6 <3/6 < 4/6< 5/6 …..< 20/6 < 21/6
So This way we can easy find the rational
numbers

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