Question -
Answer -
(i) 2/3 and 4/5
Let us make the denominators same, say 60
i.e., 2/3 and 4/5 can be written as:
2/3 = (2 ├Ч 20)/(3 ├Ч 20) = 40/60
4/5 = (4 ├Ч 12)/(5 ├Ч 12) = 48/60
Five rational numbers between 2/3 and 4/5 = five rational numbers between 40/60 and 48/60
Therefore, Five rational numbers between 40/60 and 48/60 = 41/60, 42/60, 43/60, 44/60, 45/60
(ii) -3/2 and 5/3
Let us make the denominators same, say 6
i.e., -3/2 and 5/3 can be written as:
-3/2 = (-3 ├Ч 3)/(2├Ч 3) = -9/6
5/3 = (5 ├Ч 2)/(3 ├Ч 2) = 10/6
Five rational numbers between -3/2 and 5/3 = five rational numbers between -9/6 and 10/6
Therefore, Five rational numbers between -9/6 and 10/6 = -1/6, 2/6, 3/6, 4/6, 5/6
(iii) ┬╝ and ┬╜
Let us make the denominators same, say 24.
i.e., ┬╝ and ┬╜ can be written as:
┬╝ = (1 ├Ч 6)/(4 ├Ч 6) = 6/24
┬╜ = (1 ├Ч 12)/(2 ├Ч 12) = 12/24
Five rational numbers between ┬╝ and ┬╜ = five rational numbers between 6/24 and 12/24
Therefore, Five rational numbers between 6/24 and 12/24 = 7/24, 8/24, 9/24, 10/24, 11/24