Question

which set of fractions could you use to subtract \\(\frac{7}{18} - \frac{1}{6}\\)?

\\(\bigcirc \frac{7}{18} - \frac{1}{18}\\)
\\(\bigcirc \frac{2}{6} - \frac{1}{6}\\)
\\(\bigcirc \frac{7}{18} - \frac{3}{18}\\)
\\(\bigcirc \frac{4}{6} - \frac{1}{6}\\)

Explanation:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Common Denominator",
"Equivalent Fractions"
],
"new_concepts": [
"Fraction Subtraction"
],
"current_concepts": [
"Common Denominator",
"Equivalent Fractions",
"Fraction Subtraction"
]
}
</pre_analysis>

<reasoning>

Find a common denominator

\[
\text{LCM}(18, 6) = 18
\]

Convert to equivalent fractions

\[
\frac{1}{6} = \frac{1 \times 3}{6 \times 3} = \frac{3}{18}
\]

Rewrite the subtraction expression

\[
\frac{7}{18} - \frac{1}{6} = \frac{7}{18} - \frac{3}{18}
\]
</reasoning>

<answer>
<mcq-option>(A) \(\frac{7}{18} - \frac{1}{18}\)</mcq-option>
<mcq-option>(B) \(\frac{2}{6} - \frac{1}{6}\)</mcq-option>
<mcq-correct>(C) \(\frac{7}{18} - \frac{3}{18}\)</mcq-correct>
<mcq-option>(D) \(\frac{4}{6} - \frac{1}{6}\)</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Fraction Subtraction"
]
}
</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": [
"Common Denominator",
"Equivalent Fractions"
],
"new_concepts": [
"Fraction Subtraction"
],
"current_concepts": [
"Common Denominator",
"Equivalent Fractions",
"Fraction Subtraction"
]
}
</pre_analysis>

<reasoning>

Find a common denominator

\[
\text{LCM}(18, 6) = 18
\]

Convert to equivalent fractions

\[
\frac{1}{6} = \frac{1 \times 3}{6 \times 3} = \frac{3}{18}
\]

Rewrite the subtraction expression

\[
\frac{7}{18} - \frac{1}{6} = \frac{7}{18} - \frac{3}{18}
\]
</reasoning>

<answer>
<mcq-option>(A) \(\frac{7}{18} - \frac{1}{18}\)</mcq-option>
<mcq-option>(B) \(\frac{2}{6} - \frac{1}{6}\)</mcq-option>
<mcq-correct>(C) \(\frac{7}{18} - \frac{3}{18}\)</mcq-correct>
<mcq-option>(D) \(\frac{4}{6} - \frac{1}{6}\)</mcq-option>
</answer>

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