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प्रश्न
Insert five rational numbers between `3/5` and `2/3`.
उत्तर
LCM of denominators 5 and 3 is 15.
make the denominator of each given rational number equal to 15 i.e., the LCM.
`3/5 = (3 xx 3)/(5 xx 3) = 9/15 ` and
Since five rational numbers are required, multiply the numerator and denominator of each rational number by 5 + 1 = 6.
∴ `9/15 = (9 xx 6)/(15 xx 6) = 54/90` and `10/15 = (10 xx 6)/(15 xx 6 ) = 60/90`
∴ Required rational numbers between `3/5` and `2/3` are `55/90, 56/90,57/90, 58/90`, and `59/90`.
=`11/18, 28/45,19/35,29/45` and `59/90`
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