**Jesse, a 4th grader, finds a pattern changing a mixed number to an improper fraction**

Don started Jesse on continued fractions, which leads to an
infinite continued fraction and the Golden Mean. Don showed him where to start
(with the 1+1). And they talked about the reciprocal of a fraction 1**/**3/2
= 2/3, because 3/2 x 2/3 = 1. They did the following:

Don had Jesse keep track of the answers as improper fractions, then mixed numbers and decimals. Changing fractions to decimals was new to him, but he went a long way.

Jesse explains his method of changing an improper fraction to a mixed number. In the example below he starts with 9/5. He left out that he puts the 4 on top:

Jesse used his method for the ones above. Don never saw this before! Don had Jesse do one like 12/5 = 1 7/5, and then Don had him continue till he got a proper fraction in the mixed number 2 2/5.

Notice that the numbers they got for the continued fractions were alternating!

**Fine job, Jesse!**

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