Which sequence of fractions is in descending order (from largest to smallest)?
Aptitude
Problems on H.C.F and L.C.M
Difficulty: Easy
Choose an option
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A3/5, 5/7, 7/9
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B7/9, 5/7, 3/5
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C5/7, 7/9, 3/5
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D7/9, 3/5, 5/7
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E3/5, 7/9, 5/7
Answer
Correct Answer: 7/9, 5/7, 3/5
Explanation
Introduction / Context:Ordering fractions requires reliable comparison. The goal is to list the given three fractions in strictly descending order (largest first, smallest last).
Given Data / Assumptions:
- Fractions to compare: 7/9, 5/7, 3/5.
- All are positive proper fractions.
Concept / Approach:Use decimal approximations or cross-multiplication. For quick intuition, compare values roughly: 7/9 ≈ 0.777…, 5/7 ≈ 0.714…, 3/5 = 0.6. This suggests 7/9 > 5/7 > 3/5.
Step-by-Step Solution:
Compute decimal values: 7/9 ≈ 0.777…, 5/7 ≈ 0.714…, 3/5 = 0.6.Descending order: 0.777… > 0.714… > 0.6 ⇒ 7/9, 5/7, 3/5.Verification / Alternative check:Cross-multiplication: Compare 7/9 and 5/7: 7*7 = 49 vs 5*9 = 45 ⇒ 7/9 > 5/7. Compare 5/7 and 3/5: 5*5 = 25 vs 3*7 = 21 ⇒ 5/7 > 3/5. Chain gives 7/9 > 5/7 > 3/5.
Why Other Options Are Wrong:
- Any sequence not matching 7/9 > 5/7 > 3/5 either reverses one comparison or is fully incorrect.
Common Pitfalls:
- Assuming a larger denominator always means a smaller value without checking the numerator.
- Mixing up descending with ascending order.
Final Answer:7/9, 5/7, 3/5