How do you find a "REAL NUMBER" between pairs of numbers 3 1/3 and 3 2/3?

Method 1 One way to do this is to notice that the average of two numbers ##n## and ##m## is always between the numbers.

The average is: ##(m+n)/2## which can also be written ##1/2 (m+n)##.

So, using this way to do it, add the numbers: ##3 1/3 +3 2/3 = 7##, and now divide by ##2##: ##7 -: 2 = 3 1/2##

##3 1/2## is (the middle number) between ##3 1/3## and ##3 2/3##

Method 2

If you like working with decimal numbers, use

##3 1/3 = 3.333(3)## and ##3 2/3 = 3.666(6)## (Parentheses indicate repeated digits)

So any decimal between these will work: for example:

##3.4##, or ##3.42597## or 3.33444(4)