Math, asked by ganjiaruna1986, 4 months ago

Find the 20 rational numbers between - 5/16and13/20

Answers

Answered by Pisces12
1

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:

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Answered by Anonymous
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