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Question
Give an example and verify the following statement.
The mean of two rational numbers is rational and lies between them
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Solution
Let a = `2/11` and b = `5/6` be two rational numbers
Mean of a and b is c = `1/2("a" + "b")`
= `1/2(2/11 + 5/6)`
= `1/2(((2 xx 6) + (5 xx 11))/66)`
= `1/2 xx ((12 + 55)/66)`
= `1/2 xx 67/66`
= `67/132` is in Q.
Aslo `2/11 = (2 xx 12)/(11 xx 12)`
= `24/132`
`5/6 = (5 xx 22)/(6 xx 22)`
= `110/132`
∴ `24/132 < 67/132 < 110/132`
∴ The mean lies between the given rational numbers `2/11` and `5/6`
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