## Wednesday, April 10, 2013

### Ordering fractions

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= 15*11/12*15

13/15=12*13/12*15

15*11=165

12*13=156

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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