Question

Give an example and verify the following statement.

The mean of two rational numbers is rational and lies between them

Answer 1

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`