Simplify: $5793405 \times 9999$

### Concept & Strategy When multiplying a number by a series of 9s (like $99$, $999$, $9999$), use the distributive property by representing the multiplier as a power of 10 minus 1. ### Step-by-Step Solution * **Calculation:** Rewrite $9999$ as $(10000 - 1)$: $$ 5793405 \times (10000 - 1) $$ * Distribute the multiplication: $$ (5793405 \times 10000) - (5793405 \times 1) $$ $$ 57934050000 - 5793405 $$ * Perform the final subtraction: $$ 57934050000 - 5793405 = 57928256595 $$ ### Exam Strategy & Shortcut The "Append and Subtract" shortcut is the fastest method here. Since $9999$ has four 9s, simply append four zeros to the original number ($5793405 \rightarrow 57934050000$) and then subtract the original number ($5793405$) from it. ### Common Pitfall Attempting to multiply a 7-digit number by a 4-digit number using standard long multiplication will consume minutes of exam time and almost certainly lead to a calculation error. Always look for base-10 properties. ### Final Answer Therefore, the correct answer is **57928256595**.