QUESTION IMAGE
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\\)
<pre_analysis>
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"concepts_used": [
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"Factoring Numbers",
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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>
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<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>