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complete the equations by breaking 14 into two factors. \\(14 \\times 3…

Question

complete the equations by breaking 14 into two factors.

\\(14 \times 3 = \text{select factors of 14} \times 3\\)

\\(14 \times 3 = 7 \times \square\\)

\\(14 \times 3 = \square\\)

Explanation:

Response

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"quality": "clear",
"question_count": 1,
"skills_matched": [
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"quick"
],
"needs_drawing": false,
"concepts_used": [
"Basic Multiplication",
"Factoring Numbers",
"Associative Property"
],
"new_concepts": [],
"current_concepts": [
"Basic Multiplication",
"Factoring Numbers",
"Associative Property"
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}
</pre_analysis>

<reasoning>

Factor the number 14

\[
14 = 7 \times 2
\]

Apply the associative property

\[
14 \times 3 = (7 \times 2) \times 3 = 7 \times (2 \times 3) = 7 \times 6
\]

Calculate the final product

\[
7 \times 6 = 42
\]
</reasoning>

<answer>
Complete the equations by breaking 14 into two factors:
\(14 \times 3 =\) <blank>\((7 \times 2)\)</blank> \(\times 3\)
\(14 \times 3 = 7 \times\) <blank>\(6\)</blank>
\(14 \times 3 =\) <blank>\(42\)</blank>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Associative Property"
]
}
</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": [
"Basic Multiplication",
"Factoring Numbers",
"Associative Property"
],
"new_concepts": [],
"current_concepts": [
"Basic Multiplication",
"Factoring Numbers",
"Associative Property"
]
}
</pre_analysis>

<reasoning>

Factor the number 14

\[
14 = 7 \times 2
\]

Apply the associative property

\[
14 \times 3 = (7 \times 2) \times 3 = 7 \times (2 \times 3) = 7 \times 6
\]

Calculate the final product

\[
7 \times 6 = 42
\]
</reasoning>

<answer>
Complete the equations by breaking 14 into two factors:
\(14 \times 3 =\) <blank>\((7 \times 2)\)</blank> \(\times 3\)
\(14 \times 3 = 7 \times\) <blank>\(6\)</blank>
\(14 \times 3 =\) <blank>\(42\)</blank>
</answer>

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