Problem Overview:
The task involves identifying and marking the locations of given fractions on number lines. Each fraction is provided, and we need to determine its position on the respective number line.
Solution Approach:
1.
Understand the Fraction: Each fraction is in the form \( \frac{a}{b} \), where \( a \) is the numerator and \( b \) is the denominator.
2.
Convert to Decimal (if needed): Converting the fraction to a decimal can help visualize its position on the number line.
3.
Locate on Number Line: Mark the position of the fraction on the number line based on its value.
Let's solve each problem step by step.
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1. Mark the location of \( \frac{5}{3} \)
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Fraction: \( \frac{5}{3} \)
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Decimal: \( \frac{5}{3} = 1.666\ldots \approx 1.67 \)
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Position: Between 1 and 2, closer to 2.
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Mark: At approximately 1.67.
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2. Mark the location of \( \frac{16}{7} \)
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Fraction: \( \frac{16}{7} \)
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Decimal: \( \frac{16}{7} \approx 2.2857 \)
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Position: Between 2 and 3, closer to 2.
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Mark: At approximately 2.29.
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3. Mark the location of \( \frac{13}{7} \)
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Fraction: \( \frac{13}{7} \)
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Decimal: \( \frac{13}{7} \approx 1.8571 \)
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Position: Between 1 and 2, closer to 2.
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Mark: At approximately 1.86.
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4. Mark the location of \( \frac{8}{7} \)
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Fraction: \( \frac{8}{7} \)
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Decimal: \( \frac{8}{7} \approx 1.1429 \)
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Position: Between 1 and 2, closer to 1.
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Mark: At approximately 1.14.
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5. Mark the location of \( \frac{10}{8} \)
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Fraction: \( \frac{10}{8} \)
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Simplify: \( \frac{10}{8} = \frac{5}{4} \)
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Decimal: \( \frac{5}{4} = 1.25 \)
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Position: Between 1 and 2, exactly at 1.25.
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Mark: At 1.25.
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6. Mark the location of \( \frac{10}{4} \)
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Fraction: \( \frac{10}{4} \)
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Simplify: \( \frac{10}{4} = \frac{5}{2} \)
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Decimal: \( \frac{5}{2} = 2.5 \)
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Position: Between 2 and 3, exactly at 2.5.
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Mark: At 2.5.
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7. Mark the location of \( \frac{3}{2} \)
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Fraction: \( \frac{3}{2} \)
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Decimal: \( \frac{3}{2} = 1.5 \)
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Position: Between 1 and 2, exactly at 1.5.
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Mark: At 1.5.
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8. Mark the location of \( \frac{14}{7} \)
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Fraction: \( \frac{14}{7} \)
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Simplify: \( \frac{14}{7} = 2 \)
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Position: Exactly at 2.
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Mark: At 2.
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9. Mark the location of \( \frac{6}{5} \)
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Fraction: \( \frac{6}{5} \)
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Decimal: \( \frac{6}{5} = 1.2 \)
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Position: Between 1 and 2, exactly at 1.2.
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Mark: At 1.2.
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10. Mark the location of \( \frac{11}{4} \)
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Fraction: \( \frac{11}{4} \)
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Decimal: \( \frac{11}{4} = 2.75 \)
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Position: Between 2 and 3, exactly at 2.75.
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Mark: At 2.75.
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Final Answer:
The positions of the fractions on the number lines are marked as follows:
1. \( \frac{5}{3} \approx 1.67 \)
2. \( \frac{16}{7} \approx 2.29 \)
3. \( \frac{13}{7} \approx 1.86 \)
4. \( \frac{8}{7} \approx 1.14 \)
5. \( \frac{10}{8} = 1.25 \)
6. \( \frac{10}{4} = 2.5 \)
7. \( \frac{3}{2} = 1.5 \)
8. \( \frac{14}{7} = 2 \)
9. \( \frac{6}{5} = 1.2 \)
10. \( \frac{11}{4} = 2.75 \)
\[
\boxed{\text{See markings above}}
\]
Parent Tip: Review the logic above to help your child master the concept of fractions on a number line worksheet free.
