What is $786$ times $964$?

Concept & Strategy This requires calculating the product of two 3-digit numbers. The distributive property helps simplify the math by rounding one number to the nearest thousand. Step-by-Step Solution * The problem asks for the product: $$786 \times 964$$ * Express $964$ in terms of a base of $1000$ to simplify the multiplication: $$964 = 1000 - 36$$ * Substitute this into the expression: $$786 \times (1000 - 36)$$ * Distribute $786$: $$(786 \times 1000) - (786 \times 36)$$ $$786000 - (786 \times 36)$$ * Now, calculate $786 \times 36$. You can break this down further as $786 \times (30 + 6)$: $$786 \times 30 = 23580$$ $$786 \times 6 = 4716$$ Sum = $23580 + 4716 = 28296$ * Finally, subtract this from $786000$: $$786000 - 28296 = 757704$$ Exam Strategy & Shortcut Use the last two digits technique. We need to multiply $86 \times 64$. $86 \times 64 = 86 \times (60 + 4) = 5160 + 344 = 5504$. The last two digits of the answer must be $04$. Looking at the given choices: (a) ends in $04$ (b) ends in $64$ (c) ends in $76$ (d) ends in $44$ Option (a) is the only specific numerical choice that matches. Common Pitfall Attempting rote column multiplication without checking the unit and tens digits first costs valuable time. Always scan the options to see if a partial calculation can reveal the answer. Final Answer **Therefore, the correct answer is 757704.**