find five rational numbers between 2 and 1
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Step-by-step explanation:
Five rational numbers between 1 and 2 are 11/10, 12/10, 13/10, 14/10, and 15/10.
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Step 1: Rational number between 1 and 2 = (1+2)/2 = 3/2 R
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
Therefore required integers are, 9/8, 5/4, 3/2, 7/4, 15/8.
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