Question

insert 7 rational numbers between 1/6 and 5/21

Answer 1

Without loss of generality or without

loss of fractional value we can multiply

or divide the numerator or denominator

with same number.

i ) 1 /6 = ( 1 × 7 ) / ( 6 × 7 ) = 7 / 42

= ( 3 × 7 ) / ( 3 × 42 ) = 21 / 126

ii ) 5 / 21 = ( 5 × 2 ) / ( 21 × 2 ) = 10 / 42

= ( 3 × 10 ) / ( 3 × 42 ) = 30 / 126

( 1 /6 = 21 / 126) , 22 / 126 , 23 / 126 , 24 / 126

, 25 / 126 , 26 / 126 , 27 / 126 , 28 / 126...,

( 5 / 12 = 30/ 126 )

Therefore ,

22 / 126 , 23 / 126 , 24 / 126 , 25 / 126,

26 / 126 , 27 / 126 , 28 /126 are

Seven rational numbers between 1/6 and 5 /21.

I hope this helps you.

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