First, you find the LCM of the denominators. For 3 and 5, the LCM is 15, so you write both fractions with 15 as the denominator: 2/3 becomes 10/15, and 3/5 becomes 9/15. Then you just add the numerators, so 10/15 + 9/15 = 19/15.
My Ma explained it like this last night, her chalk tapping our kitchen table, but I kept thinking of my father counting coins for my JEE coaching books, trying to make different amounts fit together into a whole.
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