The subtraction below is in base seven. Find the missing number. 5 1 6 2seven -2 6 4 4seven -------- 2 * 1 5 --------

I'll subtract column by column in base seven, borrowing 7 where needed.

Setup: 5162₇ − 2644₇ = 2*15₇

Column 1 (units): 2 − 4. We can't do this, so borrow 7: 2 + 7 = 9, and 9 − 4 = 5. ✔ (matches the 5 in the answer). The tens digit 6 becomes 5.

Column 2 (sevens): 5 − 4 = 1 ✔ (matches the 1 in the answer). No borrowing needed.

Column 3 (forty-nines): 1 − 6. We can't do this, so borrow 7 from the next column: 1 + 7 = 8, and 8 − 6 = 2. So the missing digit is 2. The thousands digit 5 becomes 4.

Column 4 (343s): 4 − 2 = 2 ✔ (matches the leading 2).

Check with base ten:

• 5162₇ = 5(343) + 1(49) + 6(7) + 2 = 1715 + 49 + 42 + 2 = 1808
• 2644₇ = 2(343) + 6(49) + 4(7) + 4 = 686 + 294 + 28 + 4 = 1012
• Difference: 1808 − 1012 = 796
• 2215₇ = 2(343) + 2(49) + 1(7) + 5 = 686 + 98 + 7 + 5 = 796 ✔

So the missing digit is 2, which is option A.

Tip: In base-n subtraction, when you borrow you add n (here 7), not 10. Always verify by converting to base ten, because it takes under a minute and catches mistakes.