Answer:
- 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.
