$999 \times 99 \times 9 \div 99 \div 9 \div 3 = x$

Concept & Formula This question tests the rule of sequential division. When multiple divisions occur in sequence without brackets, they evaluate strictly from left to right. A faster algebraic method is to convert sequential divisions into a single multiplication in the denominator: $$ a \div b \div c = \frac{a}{b \times c} $$ Step-by-Step Solution * Given expression: $$ 999 \times 99 \times 9 \div 99 \div 9 \div 3 $$ * Step 1: Group the multiplications in the numerator and move all the sequentially divided terms into the denominator as a product. $$ \frac{999 \times 99 \times 9}{99 \times 9 \times 3} $$ * Step 2: Cancel out the common terms in the numerator and denominator. Both contain a $99$ and a $9$. $$ \frac{999 \times (99 \times 9)}{(99 \times 9) \times 3} $$ This simplifies directly to: $$ \frac{999}{3} $$ * Step 3: Perform the final simple division. $$ \frac{999}{3} = 333 $$ Exam Strategy & Shortcut **Visual Cancellation:** Do not write anything down for this problem. Visually scan the equation from left to right. You see $\times 99$ and later $\div 99$—they cancel out. You see $\times 9$ and later $\div 9$—they cancel out. You are left strictly with $999 \div 3$, which is instantly $333$. This should take no more than 3 seconds to solve on an exam. Common Pitfall A common mistake is reading the expression right-to-left or grouping divisions incorrectly, such as treating $\div 9 \div 3$ as $\div (9 \div 3) = \div 3$, which completely alters the mathematical meaning and leads to an incorrect answer like $999$. Final Answer **Therefore, the correct answer is 333.**