Page 160 - NUMINO Challenge_C1
P. 160
28 2 The patterns of the numerators and denominators
3 The numerators increase by 1, and the are related to their sums, as shown below.
denominators decrease by 1.
1 321 5432
1 1,2,3 1,2,3,4
4 The numerators increase by 1, and the Sum 2 4 6
denominators decrease by 1.
Number of 1 3 4
Fractions
Group 123456
Sum of Numerators 2 3 4 5 6 7 There are 1 3 5 7 16 fractions until the 4th
and Denominators group, therefore the 23rd term is the 7th fraction
of the 5th group. The sums of the numerators
Number of Fractions 1 2 3 4 5 6 and denominators in the 5th group are 10, and
Group 7 there are nine fractions:
5 Group 7: 1 , 2 , 3 , 4 , 5 , 6 , 7 9 , 8 , 7 , 6 , 5 , 4 , 3 , 2 , 1
7654321 1 2 3 4 5 6 7 8 9
1 ,2 Therefore, the 23th term is the 7th fraction of the
7 5th group, which is 3 .
6 (1 2 3 4 5 6) 2 23 7
Creative Thinking p.92~p.93
Problem solving
1 The pattern of the pairs is related to the sum of 1 The relation between the number of folds and
the two numbers, as shown below. divided spaces is as shown below.
Number of Folds 1234
(1, 1) (1, 2) (2, 1) (1, 3) (2, 2) (3, 1) Number of Divided Spaces 2 4 8 16
Sum 2 3 4 Therefore, after 10 folds, the colored paper will
Number of 1 2 3 have 2 2 2 2 1,024 divided spaces.
pairs of the
same sum
Therefore, (4, 6) is the fourth pair among the 2 The first number of each group is the same as the
pairs of sum 10. Since there are
1 2 3 4 5 6 7 8 36 pairs in front of order of the group. When you look at the pattern
the pairs of sum 10, the index of (4, 6) is 40. of each group, the numbers of the first group
increase by 1, and they increase by 3 in the
second group and by 5 in the third group. Using
this pattern, the numbers of the sixth group start
with 6, and they increase by 11, which give (6, 17,
28, 39). Therefore, the third number of the sixth
group is 28.
Answer Key
3 The numerators increase by 1, and the are related to their sums, as shown below.
denominators decrease by 1.
1 321 5432
1 1,2,3 1,2,3,4
4 The numerators increase by 1, and the Sum 2 4 6
denominators decrease by 1.
Number of 1 3 4
Fractions
Group 123456
Sum of Numerators 2 3 4 5 6 7 There are 1 3 5 7 16 fractions until the 4th
and Denominators group, therefore the 23rd term is the 7th fraction
of the 5th group. The sums of the numerators
Number of Fractions 1 2 3 4 5 6 and denominators in the 5th group are 10, and
Group 7 there are nine fractions:
5 Group 7: 1 , 2 , 3 , 4 , 5 , 6 , 7 9 , 8 , 7 , 6 , 5 , 4 , 3 , 2 , 1
7654321 1 2 3 4 5 6 7 8 9
1 ,2 Therefore, the 23th term is the 7th fraction of the
7 5th group, which is 3 .
6 (1 2 3 4 5 6) 2 23 7
Creative Thinking p.92~p.93
Problem solving
1 The pattern of the pairs is related to the sum of 1 The relation between the number of folds and
the two numbers, as shown below. divided spaces is as shown below.
Number of Folds 1234
(1, 1) (1, 2) (2, 1) (1, 3) (2, 2) (3, 1) Number of Divided Spaces 2 4 8 16
Sum 2 3 4 Therefore, after 10 folds, the colored paper will
Number of 1 2 3 have 2 2 2 2 1,024 divided spaces.
pairs of the
same sum
Therefore, (4, 6) is the fourth pair among the 2 The first number of each group is the same as the
pairs of sum 10. Since there are
1 2 3 4 5 6 7 8 36 pairs in front of order of the group. When you look at the pattern
the pairs of sum 10, the index of (4, 6) is 40. of each group, the numbers of the first group
increase by 1, and they increase by 3 in the
second group and by 5 in the third group. Using
this pattern, the numbers of the sixth group start
with 6, and they increase by 11, which give (6, 17,
28, 39). Therefore, the third number of the sixth
group is 28.
Answer Key
