Question

Find five rational numbers between 1 and 2.
Answer

Answer 1

Step-by-step explanation:

1 = p/q                                               2 = p/q

5 +1 = 6                                            5 + 1 = 6  

1 = p/6                                              2 = p/6

p= 6 x 1 = 6/6                                 p = 6 x 2 = 12/6

so, the rational numbers are 7/6 , 8/6 , 9/6 , 10/6 and 11/6.

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Answer 2

$\sf \underline\red{Solution:}$

We know, one rational number between two numbers m and n = (m+n)/2

$\sf \underline{To \: find: }$

5 rational numbers between 1 and 2

Step 1: Rational number between 1 and 2

= (1+2)/2

= 3/2

Step 2: Rational number between 1 and 3/2

= (1+3/2)/2

= 5/4

Step 3: Rational number between 1 and 5/4

= (1+5/4)/2

= 9/8

Step 4: Rational number between 3/2 and 2

= 1/2 [(3/2) + 2)]

= 7/4

Step 5: Rational number between 7/4 and 2

= 1/2 [7/4 + 2]

= 15/8

Arrange all the results: 1 < 9/8 < 5/4 < 3/2 < 7/4 < 15/8 < 2

$\fbox \blue{Therefore required integers are 9/8, 5/4, 3/2, 7/4, 15/8}$