Page 31 - NUMINO Challenge_D2
P. 31
Type 3-2 Fibonacci’s ‘Greedy Procedure’
A mathematician named Fibonacci from the Middle Ages used a
“greedy procedure,” which is a method to select the greatest unit
fraction when finding unit fractions. The fraction 7 is expressed as
8
the sum of unit fractions as shown below.
The largest unit fraction smaller than 7 is 1 .
8 2
7 1 3 , and the largest unit fraction smaller than 3 is 1
8 2 8 8 4
since 1 3 1 .
4 8 3
Therefore, 7 1 1 1 .
8 2 4 8
Express the fraction 8 as the sum of different unit fractions using
9
‘greedy procedure.’
1 Since the greatest unit fraction smaller than 8 is 1 , you can express
9 2
8 1 7 . Find the greatest unit fraction smaller than 7 .
9 2 18 18
2 Express the fraction 8 as the sum of different unit fractions.
9
3 Use the method above to express 17 as the sum of different unit fractions.
18
28 NUMINO Challenge D2
A mathematician named Fibonacci from the Middle Ages used a
“greedy procedure,” which is a method to select the greatest unit
fraction when finding unit fractions. The fraction 7 is expressed as
8
the sum of unit fractions as shown below.
The largest unit fraction smaller than 7 is 1 .
8 2
7 1 3 , and the largest unit fraction smaller than 3 is 1
8 2 8 8 4
since 1 3 1 .
4 8 3
Therefore, 7 1 1 1 .
8 2 4 8
Express the fraction 8 as the sum of different unit fractions using
9
‘greedy procedure.’
1 Since the greatest unit fraction smaller than 8 is 1 , you can express
9 2
8 1 7 . Find the greatest unit fraction smaller than 7 .
9 2 18 18
2 Express the fraction 8 as the sum of different unit fractions.
9
3 Use the method above to express 17 as the sum of different unit fractions.
18
28 NUMINO Challenge D2
