Difficulty: Easy
Correct Answer: 4/5
Explanation:
Introduction / Context:
Number line comparison questions test your understanding of the relative sizes of fractions. Here you must identify which option lies strictly between 3/4 and 5/6. This is an important skill in fractions, inequalities, and ordering of rational numbers.
Given Data / Assumptions:
Concept / Approach:
To compare fractions, we can convert them to decimals or bring them to a common denominator. Since 3/4 and 5/6 are standard fractions, using decimal equivalents is quick: 3/4 = 0.75 and 5/6 ≈ 0.8333. Then we check each option to see which value lies between these two decimal numbers.
Step-by-Step Solution:
Step 1: Convert bounds to decimals. 3/4 = 0.75. Step 2: Compute 5/6 ≈ 0.8333. Step 3: Evaluate options: 3/5 = 0.6 (less than 0.75). 4/5 = 0.8 (between 0.75 and 0.8333). 7/5 = 1.4 (greater than 0.8333). 9/5 = 1.8 (greater than 0.8333). 2/3 ≈ 0.6667 (less than 0.75). Step 4: Only 4/5 has a value between 0.75 and 0.8333.
Verification / Alternative check:
Use common denominators. The least common multiple of 4 and 6 is 12. Then 3/4 = 9/12 and 5/6 = 10/12. Now, 4/5 written with denominator 60 is 48/60, which corresponds to 9.6/12. So 9/12 < 9.6/12 < 10/12, confirming that 4/5 lies between 3/4 and 5/6.
Why Other Options Are Wrong:
3/5 and 2/3 are both less than 3/4, so they are below the lower bound.
7/5 and 9/5 are both greater than 1, so they lie above 5/6 and are not between the bounds.
Common Pitfalls:
A frequent mistake is to compare only numerators or denominators without converting properly, which can be misleading. Another error is to assume that a larger denominator always means a smaller fraction, which is not true if numerators differ. Always use decimal conversion or common denominators for reliable comparison.
Final Answer:
The only fraction that lies between 3/4 and 5/6 is 4/5.
Discussion & Comments