Find five rational numbers between (i) 2/3 and 4/5
(ii) -3/2 and 5/3 (iii) 1/4 and 1/2
Solution:
We can find infinitely many rational numbers between any two given rational numbers by taking the mean of the two rational numbers.
Alternative method: We can make the denominator same for the two given rational numbers.
(i) 2/3 and 4/5
The LCM of both denominators is 15.
We shall multiply the numbers to get the denominator as a multiple of 15
Multiplying both the numerator and denominator of 2/3 by 20, we get
2/3 = 2/3 × 20/20 = 40/60
Multiplying both the numerator and denominator of 4/5 by 12, we get
4/5 = 4/5 × 12/12 = 48/60
The five rational numbers between 2/3 and 4/5 can be taken as:
41/60, 42/60, 43/60, 44/60, 45/60
(ii) -3/2 and 5/3
The LCM of both denominators is 6.
So we shall multiply the numbers to get the denominator as a multiple of 6
Multiplying both the numerator and denominator of -3/2 by 3, we get
-3/2 = -3/2 × 3/3 = -9/6
Multiplying both the numerator and denominator of 5/3 by 2, we get
5/3 = 5/3 × 2/2 = 10/6
The five rational numbers between -3/2 and 5/3 can be taken as:
-8/6, -7/6, 1, 3/6, 5/6
(iii) 1/4 and 1/2
The LCM of both numbers is 8.
So we shall multiply the numbers to get the denominator as a multiple of 8
Multiplying both the numerator and denominator of 1/4 by 8, we get
1/4 = 1/4 × 8/8 = 8/32
Multiplying both the numerator and denominator of 1/2 by 16, we get
1/2 = 1/2 × 16/16 = 16/32
The five rational numbers between 1/4 and 1/2 can be taken as:
9/32, 10/32, 11/32, 12/32, 13/32
☛ Check: Class 8 Maths NCERT Solutions Chapter 1
Video Solution:
Find five rational numbers between (i) 2/3 and 4/5 (ii) -3/2 and 5/3 (iii) 1/4 and 1/2
NCERT Solutions Class 8 Maths Chapter 1 Exercise 1.2 Question 5
Summary:
Find five rational numbers between (i) 2/3 and 4/5 (ii) -3/2 and 5/3 (iii) 1/4 and 1/2 are: (i) 41/60, 42/60, 43/60, 44/60, 45/60, (ii) -8/6, -7/6, 1, 3/6, 5/6, (iii) 9/32, 10/32, 11/32, 12/32, 13/32
☛ Related Questions:
visual curriculum