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Question
Show that `3/7` lies between `2/5` and `5/7`.
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Solution
`3/7` will lies between `2/5` and `5/7` if
`2/5>3/7>5/7` or `2/5<3/7<5/7`
Now, comparing `2/5,3/7,5/7`
L.C.M. of 5 and 7 = 35
∴ `2/5=(2xx7)/(5xx7)=14/35`
`3/7=(3xx5)/(7xx5)=15/35`
and `5/7=(5xx5)/(7xx5)=25/35`
∴ `14/35<15/35<25/35`
`2/5<3/7<5/7`
`3/7` lies between `2/5` and `5/7`
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