Arrange the fractions 3/4, 5/12, 13/16, 16/29 and 3/8 in ascending order of magnitude.

Introduction / Context:
This question is another exercise in ordering fractions. Here you must compare five different fractions, some of which have fairly different denominators, and then arrange them from smallest to largest.

Given Data / Assumptions:

• Fractions: 3/4, 5/12, 13/16, 16/29 and 3/8.
• We need the ascending (increasing) order.
• All fractions are positive.

Concept / Approach:
There are two practical methods: converting to decimal approximations or using a common denominator. Because one denominator is 29, decimals give a faster comparison here, while still being accurate enough.

Step-by-Step Solution:

Verification / Alternative check:
Although using a common denominator is possible, it would require the least common multiple of 4, 12, 16, 29 and 8, which is large. Using decimal approximations is acceptable as long as we are careful to keep enough precision.

Why Other Options Are Wrong:
Option a contains 16/19 instead of 16/29, which does not match the original list. Options c and d place 13/16 before 3/4, but 0.8125 is larger than 0.75, so this is incorrect. Only option b correctly preserves the ascending order based on actual values.

Common Pitfalls:
Candidates sometimes misread 16/29 as 16/19 or approximate decimals too roughly, which can change the ordering of close fractions. Staying organized and writing decimals with at least four decimal places avoids such errors.

Final Answer:
The correct ascending order of the given fractions is 3/8 < 5/12 < 16/29 < 3/4 < 13/16.