Question

a recipe calls for \\(\frac{1}{3}\\) cup of water. if the recipe is being tripled, how much water should be used?

• 1 cup
• \\(\frac{1}{9}\\) cup
• \\(\frac{1}{3}\\) cup
• 3 cups

Explanation:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Arithmetic"
],
"new_concepts": [
"Fraction Multiplication"
],
"current_concepts": [
"Arithmetic",
"Fraction Multiplication"
]
}
</pre_analysis>

<reasoning>

Identify the given values and operation

\[
\text{Original amount} = \frac{1}{3}\text{ cup}
\]
\[
\text{Scaling factor} = 3
\]

Calculate the tripled amount

\[
\text{Tripled amount} = \frac{1}{3} \times 3 = 1\text{ cup}
\]
</reasoning>

<answer>
<mcq-correct>(A) 1 cup</mcq-correct>
<mcq-option>(B) \(\frac{1}{9}\) cup</mcq-option>
<mcq-option>(C) \(\frac{1}{3}\) cup</mcq-option>
<mcq-option>(D) 3 cups</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Arithmetic",
"Fraction Multiplication"
]
}
</post_analysis>

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Arithmetic"
],
"new_concepts": [
"Fraction Multiplication"
],
"current_concepts": [
"Arithmetic",
"Fraction Multiplication"
]
}
</pre_analysis>

<reasoning>

Identify the given values and operation

\[
\text{Original amount} = \frac{1}{3}\text{ cup}
\]
\[
\text{Scaling factor} = 3
\]

Calculate the tripled amount

\[
\text{Tripled amount} = \frac{1}{3} \times 3 = 1\text{ cup}
\]
</reasoning>

<answer>
<mcq-correct>(A) 1 cup</mcq-correct>
<mcq-option>(B) \(\frac{1}{9}\) cup</mcq-option>
<mcq-option>(C) \(\frac{1}{3}\) cup</mcq-option>
<mcq-option>(D) 3 cups</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Arithmetic",
"Fraction Multiplication"
]
}
</post_analysis>