Question

Write down a fraction whose value lies between 3 and 4; whose denominator is a multiple of 5; whose numerator is a multiple of 11, and whose denominator is less than 17. How many can you find? This may look hard, so instead, try the following sequence derived from it: Write down a fraction whose value lies between 3 and 4. Write down a fraction whose value lies between 3 and 4 and whose denominator is a multiple of 5; find a way to write down all such fractions.

Answer 1

33/10 and 55/15

Explanation:

Possible denominators that are multiples of 5 less than 17 are 5, 10, 15.

Corresponding numerator ranges are [15, 20], [30, 40], and [45, 60]. In only two of these ranges are there any multiples of 11.

33 in [30, 40]

55 in [45, 60]

So, there are only two possible fractions meeting your requirement:

33/10 and 55/15