Final answer:
To find halfway between two fractions, you find their average. The average of 10/11 and 1/5 is 61/110, but none of the given options precisely match this average. The closest option to the average is 9/22.
Step-by-step explanation:
To find a rational number halfway between 10/11 and 1/5, you first need to find the average of these two numbers. This involves adding them together and then dividing by 2:
- Add the fractions: (10/11) + (1/5).
- To add fractions, they must have a common denominator. The least common multiple (LCM) of 11 and 5 is 55, so we convert the fractions:
- (10/11) becomes (50/55) and (1/5) becomes (11/55).
- Now add them: (50/55) + (11/55) = (61/55).
- Find the average by dividing the sum by 2: (61/55) / 2 = (61/55) * (1/2) = 61/110.
To simplify this, we divide the numerator and the denominator by their greatest common divisor, which is 1 in this case. The fraction 61/110 cannot be simplified further, so now we need to find which option is equivalent to 61/110.
Looking at the options, 9/22 is the one that is equivalent to 61/110 because when you multiply both the numerator and denominator of 9/22 by 5, you get 45/110. This is not equal to 61/110, and thus none of the given options is precisely halfway between 10/11 and 1/5. However, if we had to choose the closest one to 61/110, it would be 9/22.