Question

add.

\\\frac{2}{-5} + \frac{7}{6}\\

write your answer as a fraction in simplest form.

Explanation:

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"new_concepts": [
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<reasoning>

Rewrite the negative fraction

\[
\frac{2}{-5} = -\frac{2}{5}
\]

Find a common denominator

\[
\text{LCM}(5, 6) = 30
\]
\[
-\frac{2}{5} = -\frac{2 \times 6}{5 \times 6} = -\frac{12}{30}
\]
\[
\frac{7}{6} = \frac{7 \times 5}{6 \times 5} = \frac{35}{30}
\]

Add the fractions

\[
-\frac{12}{30} + \frac{35}{30} = \frac{-12 + 35}{30} = \frac{23}{30}
\]
</reasoning>

<answer>
Add.
\[ \frac{2}{-5} + \frac{7}{6} \]
Write your answer as a fraction in simplest form.
<blank>\(\frac{23}{30}\)</blank>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Fraction Addition"
]
}
</post_analysis>

Answer:

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"step_cot",
"blank_filling_formatter",
"explain_then_answer",
"quick"
],
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"concepts_used": [
"Common Denominators"
],
"new_concepts": [
"Fraction Addition",
"Signed Fractions"
],
"current_concepts": [
"Common Denominators",
"Fraction Addition",
"Signed Fractions"
]
}
</pre_analysis>

<reasoning>

Rewrite the negative fraction

\[
\frac{2}{-5} = -\frac{2}{5}
\]

Find a common denominator

\[
\text{LCM}(5, 6) = 30
\]
\[
-\frac{2}{5} = -\frac{2 \times 6}{5 \times 6} = -\frac{12}{30}
\]
\[
\frac{7}{6} = \frac{7 \times 5}{6 \times 5} = \frac{35}{30}
\]

Add the fractions

\[
-\frac{12}{30} + \frac{35}{30} = \frac{-12 + 35}{30} = \frac{23}{30}
\]
</reasoning>

<answer>
Add.
\[ \frac{2}{-5} + \frac{7}{6} \]
Write your answer as a fraction in simplest form.
<blank>\(\frac{23}{30}\)</blank>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Fraction Addition"
]
}
</post_analysis>