I'm stumped with a math question...please help

Hmm, I guess my answer would be "never". There are some situations where it may look strange to not reduce the fraction, but it isn't required. For example, 1/4 - 1/4 = 0/4. This is valid, but most people would just write '0' rather then '0/4'. You could say the same thing for '8/4'

The only time the denominator needs to change, is when the fraction cannot be expressed otherwise, such as '1.5/4' should be '3/8'. However unless my definition of 'like fractions' is wrong, this answer never exists when only adding or subtracting.

or if you need to express a "lowest common denominator" , such as 7/11 +9/23+7/13=.

In that case we usually multiply the numbers to acquire a lowest common denominator so that we can add them as fractions. Of course , with squirrely fractions as those above, I d just as soon have them converted to decimals.


You frequently see these kinds of fractions in old time surveyed maps or mining claim maps where units are always different between turning points or claims boundaries.(NTM, that old surveying units were in chains and fractions of chains)
The electronic distance measurement equipment always records and corrects distance fractions as complex decimals , so that we can determone errors of closure.(How "off" is our surveyed path or the surveyed boundary of a piece of land.

SOrry for the arcane example, but the teacher in me always has to explain basic math concepts in terms of where they are frequently used in my work.

How about 1/4 + 1/4 = 1/2?