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13 is the whole number, so 13 X 3/8kg packs = 39/8. She originally had 5kg = 40/8kg. 40/8 - 39/8 = 1/8.
Because the 1/3 remainder shown in the answer I posted does not give the exact value, multiplying it to the exact value of 3/8 kg per pack gives you the exact remainder, which is 1/8. as you explained above.
Hope this makes things a little more clear? Sorry about the original post.