Both Jenna and Mia arrived at the same answer, 170, because they are both applying the distributive property of multiplication correctly to a mathematical expression involving addition.
Jenna's Method
- Jenna first expresses the original expression as \(5(30 + 4)\).
- She then applies the distributive property, breaking it down into \(5(30) + 5(4)\).
- Finally, she calculates \(150 + 20\), which equals 170.
Mia's Method
- Mia simplifies the expression directly by recognizing that \(30 + 4 = 34\).
- She multiplies \(5\) by \(34\) to arrive at \(5(34)\).
- This yields \(170\) directly.
Comparison and Advantages
- Both methods are valid and arrive at the same result because \(5(30 + 4)\) can be simplified either by distributing the multiplication across the addition (Jenna's method) or by simplifying the expression inside the parentheses first (Mia's method).
Advantage of One Method over the Other:
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Jenna's method is beneficial in cases where breaking down the multiplication can help to clarify the process or is necessary for more complex expressions. It explicitly shows how the terms interact through distribution, which can reinforce understanding of the distributive property.
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Mia's method is often faster and more straightforward for simple calculations. It allows for quick mental math, as she combines the addends first, which might be easier for some people, especially with straightforward numbers.
In general, choosing between the two methods can depend on the context, the complexity of the numbers involved, and personal preference for how to approach multiplication and addition.