Belajar Asas Abakus Bahagian 10

Sambungan belajar abakus, Adik-adik ingin ingin belajar abakus, mari belajar di sini:

Belajar Asas Abakus Bahagian 9

Sambungan belajar abakus, Adik-adik ingin ingin belajar abakus, mari belajar di sini:

Surprising Number Patterns II

Here are some more charmers of mathematics that depend on the surprising nature of its number system. Again, not many words are needed to demonstrate the charm, for it is obvious at first sight. Just look, enjoy, and share these amazing properties with your students. Let them appreciate the patterns and, if possible, try to look for an “explanation” for this.
12345679 x 9 = 111 111 111
12345679 x18 = 222 222 222
12345679 x 27 = 333 333 333
12345679 x 36 = 444 444 444
12345679 x 45 = 555 555 555
12345679 x 54 = 666 666 666
12345679 x 63 = 777 777 777
12345679 x 72 = 888 888 888
12345679 x 81 = 999 999 999

In the following pattern chart, notice that the first and last digits of the products are the digits of the multiples of 9.
987654321 x 9 = 08 888 888 889
987654321 x 18 = 17 777 777 778
987654321 x 27 = 26 666 666 667
987654321 x 36 = 35 555 555 556
987654321 x 45 = 44 444 444 445
987654321 x 54 = 53 333 333 334
987654321 x 63 = 62 222 222 223
987654321 x 72 = 71 111 111 112
987654321 x 81 = 80 000 000 001

Surprising Number Patterns I

There are times when the charm of mathematics lies in the surprising nature of its number system. There are not many words needed to demonstrate this charm. It is obvious from the patterns attained. Look, enjoy, and
spread these amazing properties to your students. Let them appreciate the patterns and, if possible, try to look for an “explanation” for this. Most important is that the students can get an appreciation for the beauty in these number patterns.
1 x 1 = 1
11 x 11 = 121
111 x 111 = 12 321
1 111 x 1 111 = 1 234 321
11 111 x 11 111 = 123 454 321
111 111 x 111 111 = 12 345 654 321
1 111 111 x 1 111 111 = 1 234 567 654 321
11 111 111 x 11 111 111 = 123 456 787 654 321
111 111 111 x 111 111 111 = 12 345 678 987 654 321

The Beauty in Numbers 3
1 x 8 + 1 = 9
12 x 8 + 2 = 98
123 x 8 + 3 = 987
1 234 x 8 + 4 = 9 876
12 345 x 8 + 5 = 98 765
123 456 x 8 + 6 = 987 654
1 234 567 x 8 + 7 = 9 876 543
12 345 678 x 8 + 8 = 98 765 432
123 456 789 x 8 + 9 = 987 654 321