Question

21,853 Learners found this answer helpful

use the cross product property to determine whether or not the following equations are proportions:

\\(\frac{10}{3} \div 25 = 2 \div 15\\)

Explanation:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Cross Product Property",
"Proportions"
],
"new_concepts": [],
"current_concepts": [
"Proportions",
"Ratios",
"Cross Product Property"
]
}
</pre_analysis>

<reasoning>

Write the given ratios as fractions

\[
\frac{10}{3} \quad \text{and} \quad \frac{2}{15}
\]

Apply the cross product property

\[
10 \times 15 = 150
\]
\[
3 \times 2 = 6
\]

Compare the cross products

\[
150
eq 6
\]
</reasoning>

<answer>
not a proportion
</answer>

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

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Cross Product Property",
"Proportions"
],
"new_concepts": [],
"current_concepts": [
"Proportions",
"Ratios",
"Cross Product Property"
]
}
</pre_analysis>

<reasoning>

Write the given ratios as fractions

\[
\frac{10}{3} \quad \text{and} \quad \frac{2}{15}
\]

Apply the cross product property

\[
10 \times 15 = 150
\]
\[
3 \times 2 = 6
\]

Compare the cross products

\[
150
eq 6
\]
</reasoning>

<answer>
not a proportion
</answer>

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