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प्रश्न
Insert two rational numbers between the following rational numbers:
`3/5` and `5/6`
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उत्तर
Given: Insert two rational numbers between the rational numbers `3/5` and `5/6`.
Step-wise calculation:
1. Find a rational number between `3/5` and `5/6` using the formula for the average of two rational numbers:
A rational number between `3/5` and `5/6 = (3/5 + 5/6)/2`
= `(18/30 + 25/30)/2`
= `43/30 xx 1/2`
= `43/60`
Since `3/5 < 43/60 < 5/6, 43/60` is a rational number between the given two.
2. Now, find a rational number between `43/60` and `5/6`:
A rational number between `43/60` and `5/6`
= `(43/60 + 5/6)/2`
= `(43/60 + 50/60)/2`
= `93/60 xx 1/2`
= `93/120`
Since `43/60 < 93/120 < 5/6, 93/120` is also a rational number between the given two.
Two rational numbers between `3/5` and `5/6` are `43/60` and `93/120`.
