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lets use the associative property to help us solve \\(3 \\times 18\\). …

Question

lets use the associative property to help us solve \\(3 \times 18\\).

complete the equations by breaking 18 into two smaller factors.

\\(3 \times 18 = 3 \times\\) select factors of 18
\\(3 \times 18 = \square \times 6\\)
\\(3 \times 18 = \square\\)

Explanation:

Response

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

<reasoning>

Factor the number 18

\[
18 = 3 \times 6
\]

Apply the associative property

\[
3 \times 18 = 3 \times (3 \times 6) = (3 \times 3) \times 6 = 9 \times 6
\]

Calculate the final product

\[
9 \times 6 = 54
\]
</reasoning>

<answer>
Let's use the associative property to help us solve \(3 \times 18\).

Complete the equations by breaking 18 into two smaller factors.

\(3 \times 18 = 3 \times\) <blank>\((3 \times 6)\)</blank>
\(3 \times 18 =\) <blank>\(9\)</blank> \(\times 6\)
\(3 \times 18 =\) <blank>\(54\)</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": [
"Associative Property",
"Factoring Numbers",
"Basic Multiplication"
],
"new_concepts": [],
"current_concepts": [
"Associative Property",
"Factoring Numbers",
"Basic Multiplication"
]
}
</pre_analysis>

<reasoning>

Factor the number 18

\[
18 = 3 \times 6
\]

Apply the associative property

\[
3 \times 18 = 3 \times (3 \times 6) = (3 \times 3) \times 6 = 9 \times 6
\]

Calculate the final product

\[
9 \times 6 = 54
\]
</reasoning>

<answer>
Let's use the associative property to help us solve \(3 \times 18\).

Complete the equations by breaking 18 into two smaller factors.

\(3 \times 18 = 3 \times\) <blank>\((3 \times 6)\)</blank>
\(3 \times 18 =\) <blank>\(9\)</blank> \(\times 6\)
\(3 \times 18 =\) <blank>\(54\)</blank>
</answer>

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