Class Notes: Placing Fractions on a Number Line

Objective

Learn how to accurately locate and place fractions on a number line.

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Key Concepts

• Proper Fraction: A fraction less than 1 (e.g., 2/3, 1/4).
• Number Line Segment: For proper fractions, focus on the section between 0 and 1.

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Steps to Place a Fraction on a Number Line

1. Identify the Denominator

   • The denominator tells you into how many equal parts to divide the segment between 0 and 1.

2. Divide the Number Line

   • Split the segment between 0 and 1 into that number of equal parts.

3. Label Each Division

   • Starting from 0 (which is equivalent to 0/denominator), each mark represents an incremented numerator.

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Examples

Example 1: Place ( \frac{2}{3} ) on a Number Line

• Denominator = 3: Divide 0–1 into 3 equal parts.
• Marks:
  • 0 (0/3)
  • 1/3
  • 2/3 ← Target Fraction
  • 1 (3/3)

Example 2: Place ( \frac{1}{4} ) on a Number Line

• Denominator = 4: Divide 0–1 into 4 equal parts.
• Marks:
  • 0 (0/4)
  • 1/4 ← Target Fraction
  • 2/4 (or 1/2)
  • 3/4
  • 1 (4/4)

Example 3: Place ( \frac{3}{5} ) on a Number Line

• Denominator = 5: Divide 0–1 into 5 equal parts.
• Marks:
  • 0 (0/5)
  • 1/5
  • 2/5
  • 3/5 ← Target Fraction
  • 4/5
  • 1 (5/5)

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Summary

• Always split the segment between 0 and 1 according to the denominator.
• Label each point incrementally with numerators.
• The numerator tells you how many steps to count from 0.

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Practice

Try placing the following on a number line:

• ( \frac{2}{6} )
• ( \frac{4}{7} )
• ( \frac{5}{8} )