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To solve this problem using the equation \( b/8 + 25 = 500 \), you would perform the following operations:
1. Subtraction: You would subtract 25 from 500 to find out how many beads Niel had after making the necklaces but before buying additional beads.
2. Division: You would then divide the resulting number by 8 to find out how many beads he originally had per necklace (since he made 8 identical necklaces).
Therefore, the correct operations needed to solve this problem are:
subtraction and division