Fibonacci - RosemaryGeorges/Group-Wiki-Project-3 GitHub Wiki

Fibonacci Fraction

Leonardo Fibonacci was born in Pisa, Italy around 1170. Fibonacci's father was in charge of a trading post in Bugia, this is where he learned the Hindu-Arabic numeral system. Later in life Fibonacci traveled through the Mediterranean to study under some of the leading Arab mathematicians of that time. He returned from his travels in 1200 and proceeded to publish his book the Liber Abaci in 1202.

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In the Liber Abaci, an Arabic book, Fibonacci implements a way of dividing with a double-digit denominator broken up into several single digit ones. He broke down the denominator into multiples to make dividing easier. He used the remainders as he was dividing to create new fractions with the multiples. He added all of those fractions and that was the remainder of the final product forming an improper fraction. Example: 749/75

  • He will next break up the denominator into (3)(5)(5)

749/(3)(5)(5)

  • He will then divide the 749 by 3

749/3 = 249 remainder 2

  • He takes that remainder of 2 and places it in the numerator above the 3.

(2)/(3)(5)(5)

  • Next, he will take the 249 and divide it by the second number in the denominator,5.

249/5 = 49 remainder 4

  • Now he will take that remainder 4 and put it in the numerator above the 5.

(2)(4)/(3)(5)(5)

  • Next, he will take the 49 and divide it by the final number in the denominator, 5.

49/5 = 9 remainder 4

  • Then he will stick that 4 into the numerator above that last 5, as well as put the final 9 as an improper fraction. (Fibonacci reversed his improper fractions putting the whole number after.)

[(2)(4)(4)/(3)(5)(5)]9

  • The fractions will then all be added. The final numerator will be over the entire 75, the second to last is the 75 divided by the 3, then the first numerator is over the final 5.

(2/3)+(4/25)+(4/75) = 74/79

  • The final answer is:

(74/75)9 or 9(74/75)

Citation for example:

Ballew, Pat. Some Notes on Division, and Its History, 17 Nov. 2019, https://pballew.blogspot.com/2019/11/some-notes-on-division-and-its-history.html. Citation for website containing the background information and the picture:

“Fibonacci - the Story of Leonardo of Pisa.” Fibonicci, 29 Oct. 2020, https://www.fibonicci.com/fibonacci/.