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Question
Use the method of average to write 2 rational numbers between `14/5` and `16/3`
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Solution
The average of a and b is `1/2("a" + "b")`
The average of `14/5` and `16/3` is C1 = `1/2(14/5 + 16/3)`
C1 = `1/2((42 + 80)/15)`
C1 = `122/30`
C1 = `61/15`
`14/5 < 61/15 < 16/3` ....(1)
The average of `14/5` and `61/15` is C2 = `1/2(14/5 + 61/15)`
C2 = `1/2 xx ((42 + 61)/15)`
C2 = `1/2 xx 103/15 = 103/30`
∴ `14/5 < 103/30 < 61/15` ....(2)
From (1), (2) we get, `14/5 < 103/30 < 61/15 < 16/3`
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