two different subtraction problems that use only odd numbers for numerators and each have different of 3/4.

3/2 - 3/4 5/3 - 11/12 5/4 - 1/2 7/5 - 13/20 5/6 - 1/2 9/7 - 15/28 9/8 - 3/8 9/10 - 3/20 9/11 - 3/44

Step-by-step explanation:

We did a systematic search for subtraction problems of this type, eliminating ones that are too trivial, such as 1/1 - 1/4 and equivalents of those with integers added, such as 3/1 - 9/4. Even so, there are an infinite number of possibilities. some of the ones involving larger numbers in the range we looked at include ...

41/45 - 29/180 41/49 - 17/196 41/53 - 5/212

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A reasonable approach to doing this by hand seems to be to choose a denominator for the minuend, then a denominator 4 times that value for the subtrahend. Express 3/4 using the latter denominator, and find two numbers that differ by that numerator, one of which is divisible by 4, but not by 8.

Example: Choose 13 as the minuend denominator. Then 52 is the subtrahend denominator, and the difference you need to create is 39/52. The smallest odd number we can add to 39 to make it divisible by 4 but not 8 is 5. So, we can use (39+5) / 52 and 5/52 as our numbers that differ by 3/4. In reduced form, that subtraction is ...

11/13 - 5/52

Note that if you choose an even denominator, then the exact procedure will vary depending on what power of 2 is a factor of the denominator.