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QUESTION IMAGE

plot the fraction on the number line. \\(\\frac{7}{5}\\)

Question

plot the fraction on the number line. \\(\frac{7}{5}\\)

Explanation:

Response

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"concepts_used": [],
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"Fractions on Number Line",
"Improper Fractions"
],
"current_concepts": [
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"Improper Fractions"
]
}
</pre_analysis>

<reasoning>

Convert the fraction to a mixed number

\[
\frac{7}{5} = 1 \frac{2}{5}
\]

Determine the interval division

\[
\text{Each unit interval is divided into } 5 \text{ equal parts (ticks at intervals of } 0.2\text{).}
\]

Locate the point on the number line

\[
1 \frac{2}{5} = 1 + 2 \times 0.2 = 1.4
\]
\[
\text{The point must be located at the second tick mark to the right of } 1\text{.}
\]
</reasoning>

<answer>
<mcq-option>(A) Point plotted at \(\frac{4}{5}\) (four ticks to the right of 0)</mcq-option>
<mcq-option>(B) Point plotted at \(1\frac{4}{5}\) (four ticks to the right of 1)</mcq-option>
<mcq-correct>(C) Point plotted at \(1\frac{2}{5}\) (two ticks to the right of 1)</mcq-correct>
<mcq-option>(D) Point plotted at \(\frac{2}{5}\) (two ticks to the right of 0)</mcq-option>
</answer>

<plot>
{
"elements": [
{
"type": "line",
"params": [[-1, 0], [11, 0]],
"properties": {
"strokeColor": "#583C87",
"strokeWidth": 2,
"fixed": true
}
},
{
"type": "point",
"params": [[0, 0]],
"properties": {
"name": "0",
"size": 3,
"color": "#583C87",
"fixed": true,
"labelPosition": "down"
}
},
{
"type": "point",
"params": [[5, 0]],
"properties": {
"name": "1",
"size": 3,
"color": "#583C87",
"fixed": true,
"labelPosition": "down"
}
},
{
"type": "point",
"params": [[10, 0]],
"properties": {
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"size": 3,
"color": "#583C87",
"fixed": true,
"labelPosition": "down"
}
},
{
"type": "segment",
"params": [[1, -0.2], [1, 0.2]],
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"fixed": true
}
},
{
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"params": [[2, -0.2], [2, 0.2]],
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},
{
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"params": [[3, -0.2], [3, 0.2]],
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}
},
{
"type": "segment",
"params": [[7, -0.2], [7, 0.2]],
"properties": {
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{
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{…

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": true,
"concepts_used": [],
"new_concepts": [
"Fractions on Number Line",
"Improper Fractions"
],
"current_concepts": [
"Fractions on Number Line",
"Improper Fractions"
]
}
</pre_analysis>

<reasoning>

Convert the fraction to a mixed number

\[
\frac{7}{5} = 1 \frac{2}{5}
\]

Determine the interval division

\[
\text{Each unit interval is divided into } 5 \text{ equal parts (ticks at intervals of } 0.2\text{).}
\]

Locate the point on the number line

\[
1 \frac{2}{5} = 1 + 2 \times 0.2 = 1.4
\]
\[
\text{The point must be located at the second tick mark to the right of } 1\text{.}
\]
</reasoning>

<answer>
<mcq-option>(A) Point plotted at \(\frac{4}{5}\) (four ticks to the right of 0)</mcq-option>
<mcq-option>(B) Point plotted at \(1\frac{4}{5}\) (four ticks to the right of 1)</mcq-option>
<mcq-correct>(C) Point plotted at \(1\frac{2}{5}\) (two ticks to the right of 1)</mcq-correct>
<mcq-option>(D) Point plotted at \(\frac{2}{5}\) (two ticks to the right of 0)</mcq-option>
</answer>

<plot>
{
"elements": [
{
"type": "line",
"params": [[-1, 0], [11, 0]],
"properties": {
"strokeColor": "#583C87",
"strokeWidth": 2,
"fixed": true
}
},
{
"type": "point",
"params": [[0, 0]],
"properties": {
"name": "0",
"size": 3,
"color": "#583C87",
"fixed": true,
"labelPosition": "down"
}
},
{
"type": "point",
"params": [[5, 0]],
"properties": {
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"size": 3,
"color": "#583C87",
"fixed": true,
"labelPosition": "down"
}
},
{
"type": "point",
"params": [[10, 0]],
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"color": "#583C87",
"fixed": true,
"labelPosition": "down"
}
},
{
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"fixed": true
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"params": [[2, -0.2], [2, 0.2]],
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"strokeWidth": 1,
"fixed": true
}
},
{
"type": "segment",
"params": [[3, -0.2], [3, 0.2]],
"properties": {
"strokeColor": "#583C87",
"strokeWidth": 1,
"fixed": true
}
},
{
"type": "segment",
"params": [[4, -0.2], [4, 0.2]],
"properties": {
"strokeColor": "#583C87",
"strokeWidth": 1,
"fixed": true
}
},
{
"type": "segment",
"params": [[6, -0.2], [6, 0.2]],
"properties": {
"strokeColor": "#583C87",
"strokeWidth": 1,
"fixed": true
}
},
{
"type": "segment",
"params": [[7, -0.2], [7, 0.2]],
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"params": [[9, -0.2], [9, 0.2]],
"properties": {
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"fixed": true
}
},
{
"type": "point",
"params": [[7, 0]],
"properties": {
"name": "7/5",
"size": 6,
"color": "#8C55F2",
"fixed": true,
"labelPosition": "up"
}
}
],
"timestamps": [0.5]
}
</plot>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Geometry",
"Fractions on Number Line"
]
}
</post_analysis>