Ordering Fractions from Greatest to Least

Objective

Order four given fractions from greatest to least by finding a common denominator and comparing their values.

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Steps to Order Fractions

1. Find a Common Denominator

   • Multiply all unique denominators together to get a common denominator.
   • For denominators 3, 4, and 5:
     • 4 × 5 = 20
     • 20 × 3 = 60
     • Common denominator is 60.

2. Convert Each Fraction to the Common Denominator

   • Divide 60 by each fraction's original denominator to find the multiplier:

     | Original Fraction | Multiplier | New Numerator | |------------------|--------------|------------------| | 2/3 | 60 ÷ 3 = 20 | 2 × 20 = 40 | | 1/4 | 60 ÷ 4 = 15 | 1 × 15 = 15 | | 4/5 | 60 ÷ 5 = 12 | 4 × 12 = 48 | | 3/4 | 60 ÷ 4 = 15 | 3 × 15 = 45 |

   • New fractions:

     • 2/3 = 40/60
     • 1/4 = 15/60
     • 4/5 = 48/60
     • 3/4 = 45/60

3. Compare the Numerators

   • List numerators in descending order: 48, 45, 40, 15

4. Match with Original Fractions

   • 48/60 = 4/5
   • 45/60 = 3/4
   • 40/60 = 2/3
   • 15/60 = 1/4

5. Write Fractions from Greatest to Least

   • 4/5 > 3/4 > 2/3 > 1/4

6. Check with Calculator (Decimal Values)

   • 4/5 = 0.8
   • 3/4 = 0.75
   • 2/3 ≈ 0.67
   • 1/4 = 0.25

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Final Answer

Ordered from greatest to least:

4/5 > 3/4 > 2/3 > 1/4

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Key Takeaways

• To compare fractions, use a common denominator.
• Compare numerators after conversion.
• Simplify to match original fractions for your final answer.
• Optionally, verify by converting fractions to decimals.