Hi AL Rachels,
Thanks for formatting the question and the answer space very nicely. My main problem is the way I generated the question. It does not generate a wide variety of fractions that give answers as "Proper Fractions". The reason is that my logic of designing the question is not very good! I am looking for a better algorithm of designing a wide variety of proper fractions which add up to another proper fraction.
I am going to try this method:
Numbers 24, 36, 48, (56), 64, and 72 have a lot of factors.
First take pairs that add up to 24:
[2, 22], [3,21], [4,20], [6,18], [8,16], [9.15], 10,14], [12,12]
Take the first element (2) in [2,22]
Now make pairs with the second elements of the rest of pairs.
[2,21], [2,20], [2,18], [2,16], [2,15], [2,14], [2,12]
Take the first pair [2,21] and generate the two fractions using them: 2/24 + 21/24 and simplify them to generate the question.
1/12 + 7/8. The answer will be always less than 1, hence, it will be a proper fraction. This way, we can generate more than 50 different questions only with the pairs of 24.
Likewise, we can take 36, 48, etc and generate fractions. This method will generate a large number of combination of fractions.
What do you think about this method?
How ever, designing the question with all these conditions will be a bit challenging! If I succeed, I will post it to the forum. May be, it is better to design separate sets of questions with each set of numbers.