Subjects arithmetic

Missing Digit

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Search Solutions

Missing Digit


1. **State the problem:** We need to find the missing digit □ in the multiplication: 304 × 7□ The partial results and final sum are given: 2736 (which is 304 × 7) + 21280 (which is 304 × □ shifted one digit left) = 24016 So, the addition is: 2736 + 21280 = 24016 2. **Analyze the multiplication:** The first partial product, 2736, confirms that 7 × 304 = 2736. 3. **Analyze the second partial product:** It is 21280, which corresponds to 304 × the unknown digit □ multiplied by 10 (because it's shifted one digit left). Let the missing digit be $x$, so: $$304 \times x \times 10 = 21280$$ 4. **Solve for $x$:** $$304x \times 10 = 21280$$ $$3040x = 21280$$ Divide both sides by 3040: $$x = \frac{21280}{3040} = 7$$ 5. **Verify:** Calculating $304 \times 7 = 2128$, and shifted one left (multiply by 10) is 21280, which matches the partial product. 6. **Conclusion:** The missing digit □ is 7. **Final answer:** The missing digit □ = 7.