1. **State the problem:** We need to find the unknown partial products in the multiplication of 113 by 25. 2. **Recall the multiplication setup:** $$ \begin{array}{r} \phantom{+}113 \\ \times \phantom{+}25 \\ \hline ? \\ 200 \\ ? \\ 500 \\ 50 \\ + 15 \\ \hline 2,825 \end{array} $$ 3. **Understand partial products:** - Multiplying 113 by 5 (units digit of 25) gives the first partial product. - Multiplying 113 by 20 (tens digit of 25 times 10) gives the second partial product. 4. **Calculate 113 × 5:** $$113 \times 5 = 565$$ 5. **Calculate 113 × 20:** $$113 \times 20 = 2,260$$ 6. **Check the sum of partial products:** $$565 + 2,260 = 2,825$$ 7. **Match partial products to the unknowns:** - The unknown partial products are 565 and 2,260. - The given partial products 200, 500, 50, and 15 are parts of the breakdown but not the full partial products. 8. **Select the correct choices:** - 200 and 500 are parts of the breakdown but not the full partial products. - The correct unknown partial products are 600 and 2,000 (closest to 565 and 2,260), but since 600 and 2,000 are options, and 565 and 2,260 are exact, the best choices are 200 and 2,000. **Final answer:** The unknown partial products are 200 and 2,000.