Order the fractions, 4/9, 3/4, 4/5, 11/12, and 13/15, from least to greatest.
This problem is on the Khan Academy web site.
The Khan academy solves the problem in the traditional way by finding a common denominator for all five fractions and then ordering on the basis of the numerator. This is a very useful video. It teaches how to systematically find a common denominator for several fractions.
The problem could be solved quicker by an observant student.
Observe only one of the five numbers 4/9 is less than one half. 4/9 is the smallest of the five numbers.
We know that 3/4 is less than 4/5, which is less than 11/12 because 1/12 is less than 1/5, which is less than ¼.
We know that 4/5 (which is 12/15) is less than 13/15.
All we have to do is compare 11/12 to 13/15. I suspect that 11/12 is larger than 13/15 but we should compare by finding a common denominator.
11/12 is the largest of the five fractions.
The five fractions from smallest to largest are 4/9, ¾, 4/5, 13/15 and 11/12
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