Find the 20 rational numbers between - 5/16and13/20
Answers
Answer:
How to find rational numbers between two given rational numbers?
If m and n be two rational numbers such that m < n then 1/2 (m + n) is a rational number between m and n.
1. Find out a rational number lying halfway between 2/7 and 3/4.
Solution:
Required number = 1/2 (2/7 + 3/4)
= 1/2 ((8 + 21)/28)
= {1/2 × 29/28)
= 29/56
Hence, 29/56 is a rational number lying halfway between 2/7 and 3/4.
2. Find out a rational number lying between -1/3 and 1/2.
Solution:
Required number = 1/2 (-1/3 + 1/2)
= 1/2 ((-2 + 3)/6)
= {1/2 × 1/6)
= 1/12
Hence, 1/12 is a rational number lying between 1/3 and 1/2.
3. Find out ten rational numbers lying between -3/11 and 8/11.
Solution:
We know that -3 < -2 < -1 < 0 < 1 < 2 < 3 < 4 < 5 < 6 < 7 < 8
Therefore, -3 /11< -2/11 < -1/11 < 0/11 < 1/11 < 2/11 < 3/11 < 4/11 < 5/11 < 6/11 < 7/11 < 8/11
Hence, -2/11, -1/11, 0/11, 1/11, 2/11, 3/11, 4/11, 5/11, 6/11 and 7/11 are the ten rational numbers lying between -3/11 and 8/11.
4. Find out three rational numbers lying between 3 and 4.
Solution:
A rational number between 3 and 4 is 1/2 (3 + 4) = 7/2.
Then, 3 < 7/2 < 4
A rational number between 3 and 7/2 = 1/2 {3 + 7/2} = 1/2 (3/1 + 7/2)
= 1/2 ((6 + 7)/2) = (1/2 × 13/2) = 13/4
A rational number between 7/2 and 4 = 1/2 {7/2 + 4} = 1/2 (7/2 + 4/1)
= 1/2 ((7 + 8)/2) = {1/2 × 15/2} = 15/4
Therefore, 3 < 13/4 < 7/2 < 15/4 < 4
Hence, 13/4, 7/2 and 15/4 are the three rational numbers lying between 3 and 4.
Step-by-step explanation:
MARK ME BRAINLIEST