Arrange the following fractions in ascending order: 13/18, 29/36, 41/45, 51/60
2023
Arrange the following fractions in ascending order:
13/18, 29/36, 41/45, 51/60
Answer: A. 13/18 < 29/36 < 51/60 < 41/45 — ConceptTo compare positive fractions, rewrite them with a common positive denominator. Their order is then the order of their numerators. A valid common…
- A.
13/18 < 29/36 < 51/60 < 41/45
- B.
13/18 < 51/60 < 29/36 < 41/45
- C.
51/60 < 41/45 < 29/36 < 13/18
- D.
More than one of the above
- E.
None of the above
Attempted by 2 students.
Show answer & explanation
Correct answer: A
Concept
To compare positive fractions, rewrite them with a common positive denominator. Their order is then the order of their numerators.
A valid common denominator is any common multiple of all denominators; using the least common multiple keeps the numerators small.
Application
The least common multiple of 18, 36, 45, and 60 is 180.
Convert each fraction: 13/18 = 130/180, 29/36 = 145/180, 51/60 = 153/180, and 41/45 = 164/180.
Compare the numerators: 130 < 145 < 153 < 164.
Therefore, 13/18 < 29/36 < 51/60 < 41/45.
Cross-check
As a decimal check, the values are approximately 0.722, 0.806, 0.850, and 0.911 in the same ascending order.
Result
The ascending order is 13/18 < 29/36 < 51/60 < 41/45.