1. **State the problem:** Multiply 9309 by 931. 2. **Formula used:** Multiplication of two numbers is done by multiplying each digit of one number by each digit of the other and summing appropriately. 3. **Intermediate work:** Multiply 9309 by 931: $$9309 \times 931 = 9309 \times (900 + 30 + 1)$$ $$= 9309 \times 900 + 9309 \times 30 + 9309 \times 1$$ $$= 8,378,100 + 279,270 + 9,309$$ 4. **Sum the partial products:** $$8,378,100 + 279,270 = 8,657,370$$ $$8,657,370 + 9,309 = 8,666,679$$ 5. **Final answer:** $$9309 \times 931 = 8,666,679$$ This method breaks down the multiplication into simpler parts and then adds them together to get the final product.