To determine why multiplying 90 by 9,000 and then adding 90 times 100 might not be the appropriate approach, it’s important to understand the context and the underlying principles of the mathematical problem you are solving. Assuming this question arises from a particular section in a textbook or problem set, the solution likely requires a specific algebraic or arithmetic framework that applies to 5.7 Question #1.
Here are potential reasons why the described method could be incorrect:
Order of Operations: The mathematical principles concerning order of operations—PEMDAS/BODMAS (Parentheses/Brackets, Exponents/Orders, Multiplication and Division (left-to-right), Addition and Subtraction (left-to-right))—may require a different sequence of calculations.
Problem Context: The problem statement might entail different operations first, such as distributing multiplication over addition if you’re dealing with an expression like \( 90 \times (9,000 + 100) \). Ensuring you’re following the described order in the problem can affect outcomes.
Correct Mathematical Approach: The question might be assessing a particular mathematical method, such as factoring, distribution, or simplification that involves using properties of numbers or expressions which do not align with the direct approach of multiplying and then adding.
Common Traps: The problem could be designed with an intentional complexity to test if students avoid this “common mistake.” Realizing this requires sticking to guidelines or solving methods recommended by the chapter or problem set.
Unit and Context Considerations: Sometimes, values and operations need adjustments based on the problem’s units, scale, or real-world implications that straightforward multiplication and addition overlook.
For a definitive explanation, refer back to the instructions or rules given within the specific section of your material that frames the calculations for 5.7 Question #1.
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