Final answer:
The fraction we are looking for is 35/42. It fits the criteria of having an odd numerator and an even denominator between 35 and 50 and simplifies to 5/6.
Step-by-step explanation:
We are given that a fraction in its simplest form is 5/6, and we need to find the original fraction given that the numerator is odd and the denominator is even and is between 35 and 50.
To determine the fraction, we need to find a common multiple of 6 that falls within the specified range for the denominator, and then find the corresponding numerator that will reduce to 5/6.
Since 6 times 6 is 36, and that's the first multiple of 6 greater than 35, we'll start with 36 as a potential denominator.
The numerator for the fraction equivalent to 5/6 with a denominator of 36 would be 5 times 6, which equals 30.
However, 30 is even, not odd, so 36 is not the correct denominator.
The next even multiple of 6 is 42.
The corresponding numerator would be 5 times 7, which equals 35.
This fits our requirements since 35 is odd and 42 is even, and when we simplify 35/42, we get 5/6.
Therefore, the fraction we are looking for is 35/42.