1. Finding rational numbers between 2 rational numbers – Aliter method

2. Here, we take the LCM of c and d. Let the LCM be e.
Consider 2 rational numbers and
q1 q2 q3
To find the rational numbers q1, q2 and q3 between and
Convert the denominator of both the fractions in to the same denominator
by taking LCM.
Here, we take the LCM of c and d. Let the LCM be e.
Find the equivalent fraction of and using the LCM.
So,
If there is a number between the numerators a and b after taking LCM,
there is a rational number between them.

3. Example 1: Find the rational numbers between and using aliter method.
Solution: To find the rational numbers between the two fractions, we need to make
the denominators common for both the fractions.
Step 1: To make the denominators common  Find LCM of 4 and 6
LCM of 4 and 6 = 12
Step 2: Rewrite fractions and to its equivalent form using the LCM = 12.
Step 3: We have numbers between and
Therefore the rational numbers are x3 x2 x3 x2

4. Example 2: Find the rational numbers between and using aliter method.
Solution: To find the rational numbers between the two fractions, we need to make
the denominators common for both the fractions.
Step 1: To make the denominators common  Find LCM of 5 and 3
LCM of 5 and 3 = 15
Step 2: Rewrite fractions and to its equivalent form using the LCM = 18. =
Step 3: We have numbers between and
Therefore the rational numbers are x3 x5 x3 x5

5. Example 3: Find the rational numbers between and using aliter method.
Solution: To find the rational numbers between the two fractions, we need to make
the denominators common for both the fractions.
Step 1: To make the denominators common  Find LCM of 4 and 5
LCM of 4 and 5 = 20
Step 2: Rewrite fractions and to its equivalent form using the LCM = 20.
Here, we do not have numbers between and x5 x4 x5 x4

6. Sometimes after taking LCM and converting the given fractions to equivalent fractions with a common denominator, we may not get any numbers between the numerators of the equivalent fraction. Step 3: If there is no number between the numerators, then multiply the numerator and denominator by 10 to get rational numbers between them. Therefore, the rational numbers between and are
Multiplying numerator and denominator by 10
Multiplying numerator and denominator by 10
151
200
152
200
153
200
154
200
155
200
156
200
157
200
158
200
159
200

7. Try these
Find the rational numbers between 3/12 and 7/36 using aliter method