You can put this solution on YOUR website! The lowest common denominator for 2 and 5 is 10. Form the equivalent fractions for 1/2 and 3/5 in denominations of (1/10). What fractions with this denomination are or is between 1/2 and 3/5?
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So you see the next problem is you need a denomination smaller than (1/10). What denomination do you want? Try anything. Pick a small factor, like 2 so use a common denominator of maybe, , which is 20.
Now, find the equivalent fractions for (1/2) and (3/5) in denominations of (1/20). NOW you can find some choices for what rational number is between (1/2) and (3/5).