Chapter 2.4, Problem 19P

Consider the following list of fractions:

   $\frac{1}{1},\frac{2}{1},\frac{3}{2},\frac{5}{3},\frac{8}{5}$ ,….

You do not have to explain your answers to the following parts:

a. Describe a pattern in the list of fractions. Use your description to find the next 5 entries in the list after $\frac{8}{5}$ . You will now have the first 10 entries in the list of fractions.

b. Use either the cross-multiplying method or the common denominator method to compare the sizes of the 1st, 3rd, 5th, 7th, and 9th fractions in the list. Describe a pattern in the sizes of these fractions. Describe a pattern that occurs when you compare the fractions.

c. Use either the cross-multiplying method or the common denominator method to compare the sizes of the 2nd, 4th, 6th, 8th, and 10th fractions in the list. Describe a pattern in the sizes of these fractions. Describe a pattern that occurs when you compare the fractions.

d. Convert the 10 fractions on your list to decimals, and plot them on a number line. Zoom in on portions of your number line so that you can show clearly where each decimal number is plotted relative to the others.

e. If you could find more and more entries in the list of fractions, and plot them on a number line, in what region of the number line would they be located? Do you think these numbers would get closer and closer to a particular number?