Question

practice test: fractions and mixed numbers unit 2
score: 2/34 answered: 4/34
question 5
if one circle represents \one whole\, what fraction of area is shaded blue? give your answer as a mixed number.

Explanation:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"blank_filling_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Mixed Numbers",
"Fraction Representation"
],
"new_concepts": [],
"current_concepts": [
"Mixed Numbers",
"Fraction Representation"
]
}
</pre_analysis>

<reasoning>

Count the fully shaded wholes

\[
1 \text{ whole circle is completely shaded.}
\]

Determine the fractional part of the second circle

\[
\text{Total equal sectors} = 3
\]
\[
\text{Shaded sectors} = 2
\]
\[
\text{Fraction shaded} = \frac{2}{3}
\]

Combine into a mixed number

\[
1 + \frac{2}{3} = 1\frac{2}{3}
\]
</reasoning>

<answer>
If one circle represents "one whole", what fraction of area is shaded blue? Give your answer as a mixed number. <blank>\(1\frac{2}{3}\)</blank>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Arithmetic",
"Mixed Numbers"
]
}
</post_analysis>

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"blank_filling_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Mixed Numbers",
"Fraction Representation"
],
"new_concepts": [],
"current_concepts": [
"Mixed Numbers",
"Fraction Representation"
]
}
</pre_analysis>

<reasoning>

Count the fully shaded wholes

\[
1 \text{ whole circle is completely shaded.}
\]

Determine the fractional part of the second circle

\[
\text{Total equal sectors} = 3
\]
\[
\text{Shaded sectors} = 2
\]
\[
\text{Fraction shaded} = \frac{2}{3}
\]

Combine into a mixed number

\[
1 + \frac{2}{3} = 1\frac{2}{3}
\]
</reasoning>

<answer>
If one circle represents "one whole", what fraction of area is shaded blue? Give your answer as a mixed number. <blank>\(1\frac{2}{3}\)</blank>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Arithmetic",
"Mixed Numbers"
]
}
</post_analysis>