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Question
Find a rational number exactly halfway between:
`1/15` and `1/12`
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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 `1/15` and `1/12`
Here, a = `1/15` and b = `1/12`
∴ `(a + b)/2 = (1/15 + 1/12)/2`
= `((1 xx 4)/(15 xx 4) + (1 xx 5)/(12 xx 5))/2` ...[∵ LCM of 15 and 12 = 60]
= `(4/60 + 5/60)/2`
= `((4 + 5)/60)/2`
= `9/(60 xx 2)`
= `9/120`
= `3/40`
Hence, the exactly halfway between `1/15` and `1/12` is `3/40`.
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