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First divide the list into fractions larger and smaller than 1/2:
• | Smaller than 1/2: 2/5, 1/3, 1/4 |
• | Larger than 1/2: 5/8, 3/4, 2/3, 4/7 |
For those smaller than 1/2, 2/5 is larger than 1/4 (numerators three less than denominators), 1/3 is larger than 1/4 (same numerator), and 2/5 is larger than 1/3 (compare using equivalent fractions 6/15 and 5/15). The order is 1/4, 1/3, 2/5.
For those larger than 1/2, convert 3/4 and 2/3 to fractions where the numerator is three less than the denominator. (Or you may be able to visualize that 3/4 is greater than 2/3.) The list becomes 5/8, 9/12, 6/9, 4/7. This makes it easy to put the list in order: 4/7, 5/8, 6/9, 9/12.
The complete list is 1/4, 1/3, 2/5, 4/7, 5/8, 2/3, 3/4.
<< back to Problem C4
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