Question

rewrite the fraction with the indicated denominator.
\\(\frac{2}{5} = \frac{\quad}{40}\\)

\\(\circ\\ \frac{14}{40}\\)
\\(\circ\\ \frac{2}{40}\\)
\\(\circ\\ \frac{8}{40}\\)
\\(\circ\\ \frac{16}{40}\\)

Explanation:

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"new_concepts": [
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</pre_analysis>

<reasoning>

Find the scaling factor for the denominator

\[
\frac{40}{5} = 8
\]

Multiply the numerator by the scaling factor

\[
2 \times 8 = 16
\]

Write the equivalent fraction

\[
\frac{2}{5} = \frac{16}{40}
\]
</reasoning>

<answer>
<mcq-option>(A) \(\frac{14}{40}\)</mcq-option>
<mcq-option>(B) \(\frac{2}{40}\)</mcq-option>
<mcq-option>(C) \(\frac{8}{40}\)</mcq-option>
<mcq-correct>(D) \(\frac{16}{40}\)</mcq-correct>
</answer>

<post_analysis>
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"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Equivalent Fractions"
]
}
</post_analysis>

Answer:

<pre_analysis>
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"step_cot",
"multiple_choice_formatter",
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],
"new_concepts": [
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],
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]
}
</pre_analysis>

<reasoning>

Find the scaling factor for the denominator

\[
\frac{40}{5} = 8
\]

Multiply the numerator by the scaling factor

\[
2 \times 8 = 16
\]

Write the equivalent fraction

\[
\frac{2}{5} = \frac{16}{40}
\]
</reasoning>

<answer>
<mcq-option>(A) \(\frac{14}{40}\)</mcq-option>
<mcq-option>(B) \(\frac{2}{40}\)</mcq-option>
<mcq-option>(C) \(\frac{8}{40}\)</mcq-option>
<mcq-correct>(D) \(\frac{16}{40}\)</mcq-correct>
</answer>

<post_analysis>
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"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Equivalent Fractions"
]
}
</post_analysis>