Arrange the fractions 5/8, 7/12, 3/4 and 13/16 in ascending (increasing) order of magnitude.

Introduction / Context:
This problem tests your fraction comparison skills, which are crucial in many aptitude topics such as ratio, proportion and data interpretation. You are asked to arrange four fractions in ascending order, which requires understanding which is smallest and which is largest.

Given Data / Assumptions:

• Fractions: 5/8, 7/12, 3/4 and 13/16.
• We need to order them from smallest to largest.
• All numbers are positive proper fractions less than 1.

Concept / Approach:
There are two standard approaches. One is to convert each fraction to a decimal. The other is to convert fractions to a common denominator and then compare their numerators. Using decimals is intuitive, while common denominators avoid rounding issues.

Step-by-Step Solution:

Verification / Alternative check:
We may also take 48 as a common denominator (LCM of 8, 12, 4 and 16). Converting, 7/12 = 28/48, 5/8 = 30/48, 3/4 = 36/48 and 13/16 = 39/48. Comparing numerators 28, 30, 36 and 39 gives the same order.

Why Other Options Are Wrong:
Any order that puts 5/8 before 7/12 wrongly assumes 0.625 is less than 0.5833. Similarly, placing 13/16 before 3/4 is incorrect, because 0.8125 is greater than 0.75. Thus only the sequence 7/12 < 5/8 < 3/4 < 13/16 is logically correct.

Common Pitfalls:
Students sometimes compare fractions only by denominators or numerators without using a consistent method. Another error is rounding too roughly, which can reverse the correct order for close values such as 7/12 and 5/8. Using a common denominator or precise decimals avoids these mistakes.

Final Answer:
The correct ascending order of the given fractions is 7/12 < 5/8 < 3/4 < 13/16.