I am a middle school student (7th grade) and I was wondering if you could help me with ordering fractions from least to greatest the fractions are 31/12, 2 5/6 and 2 3/4.

Recent studies of how we 'do arithmetic' in our heads show that this type of ordering is DIFFERENT than doing exact calculations. In line with this, I would suggest you lay out the 'number line':

(Given the fractions involved, you MAY want to do it like a ruler with each interval divided into 12 pieces.)

Now put your numbers onto this line, for example.

When you get the numbers placed more or less correctly, you will see the 'ordering' - from left to right - as the ordering from smallest to largest. This picture of the number line will have lots of uses through you further studies in math. Many people do use such a 'picture' in their heads all the time.


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