Question

which set of fractions could you use to add \\(\frac{2}{3} + \frac{1}{4}\\)?

• \\(\frac{4}{6} + \frac{2}{8}\\)
• \\(\frac{2}{6} + \frac{1}{8}\\)
• \\(\frac{8}{12} + \frac{3}{12}\\)
• \\(\frac{2}{12} + \frac{1}{12}\\)

Explanation:

<pre_analysis>
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"concepts_used": [],
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"current_concepts": [
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}
</pre_analysis>

<reasoning>

Find the least common denominator

\[
\text{LCM}(3, 4) = 12
\]

Convert to equivalent fractions

\[

$$\begin{aligned} \frac{2}{3} &= \frac{2 \times 4}{3 \times 4} = \frac{8}{12} \\ \frac{1}{4} &= \frac{1 \times 3}{4 \times 3} = \frac{3}{12} \end{aligned}$$

\]

Write the equivalent addition expression

\[
\frac{8}{12} + \frac{3}{12}
\]
</reasoning>

<answer>
<mcq-option>(A) \(\frac{4}{6} + \frac{2}{8}\)</mcq-option>
<mcq-option>(B) \(\frac{2}{6} + \frac{1}{8}\)</mcq-option>
<mcq-correct>(C) \(\frac{8}{12} + \frac{3}{12}\)</mcq-correct>
<mcq-option>(D) \(\frac{2}{12} + \frac{1}{12}\)</mcq-option>
</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",
"explain_then_answer",
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"Common Denominator",
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"Fraction Addition"
]
}
</pre_analysis>

<reasoning>

Find the least common denominator

\[
\text{LCM}(3, 4) = 12
\]

Convert to equivalent fractions

\[

$$\begin{aligned} \frac{2}{3} &= \frac{2 \times 4}{3 \times 4} = \frac{8}{12} \\ \frac{1}{4} &= \frac{1 \times 3}{4 \times 3} = \frac{3}{12} \end{aligned}$$

\]

Write the equivalent addition expression

\[
\frac{8}{12} + \frac{3}{12}
\]
</reasoning>

<answer>
<mcq-option>(A) \(\frac{4}{6} + \frac{2}{8}\)</mcq-option>
<mcq-option>(B) \(\frac{2}{6} + \frac{1}{8}\)</mcq-option>
<mcq-correct>(C) \(\frac{8}{12} + \frac{3}{12}\)</mcq-correct>
<mcq-option>(D) \(\frac{2}{12} + \frac{1}{12}\)</mcq-option>
</answer>

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