Arrange the following fractions in ascending order :…

2023

Arrange the following fractions in ascending order :

\(\frac{13}{18},\;\frac{29}{36},\;\frac{41}{45},\;\frac{51}{60}\)

Answer: A. \(\frac{13}{18} < \frac{29}{36} < \frac{51}{60} < \frac{41}{45}\) — ConceptTo compare positive fractions, rewrite them with a common positive denominator. Their order is then the order of their numerators. A valid common…

  1. A.

    \(\frac{13}{18} < \frac{29}{36} < \frac{51}{60} < \frac{41}{45}\)

  2. B.

    \(\frac{13}{18} < \frac{51}{60} < \frac{29}{36} < \frac{41}{45}\)

  3. C.

    \(\frac{51}{60} < \frac{41}{45} < \frac{29}{36} < \frac{13}{18}\)

  4. D.

    More than one of the above

  5. E.

    None of the above

Attempted by 16 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

  1. The least common multiple of 18, 36, 45, and 60 is 180.

  2. Convert each fraction: 13/18 = 130/180, 29/36 = 145/180, 51/60 = 153/180, and 41/45 = 164/180.

  3. Compare the numerators: 130 < 145 < 153 < 164.

  4. 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.

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