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Question
Find a rational number exactly halfway between:
`1/6` and `1/9`
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Solution
We know that, a rational number, which is halfway between two rational number i.e. a and b = `(a + b)/2`
Given rational numbers are `1/6` and `1/9`
Here, a = `1/6` and b = `1/9`
∴ `(a + b)/2 = (1/6 + 1/9)/2`
= `((1 xx 3)/(6 xx 3) + (1 xx 2)/(9 xx 2))/2` ...[∵ LCM of 6 and 9 = 18]
= `(3/18 + 2/18)/2`
= `((3 + 2)/18)/2`
= `(5/18)/2`
= `5/(18 xx 2)`
= `5/36`
Hence, the exactly halfway between `1/6` and `1/9` is `5/36`.
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