Beautiful number patterns

Today is India’s National Mathematics Day, in honour of the great Indian Mathematician, Srinivasa Ramanujam (1887-1920) on his birthdate.

Ramanujam did not receive formal training in pure Math but he sought out beautiful patterns in Math. He lived in colonial India, son of a clerk and housewife. He eventually got invited to Cambridge university where he amazed the world with his many unconventional and original ideas. He lived only a short life, dying of illness at 32 years old but he made substantial contributions to many fields in Math including solving problems previously considered unsolvable. His life was made into the movie, “The man who knew infinity”, an inspiring show of a man’s quest to uncover the beauty of nature through Math. Here are some patterns by Ramanujam. Can you find other interesting number patterns?

1 x 8 + 1 = 9

12 x 8 + 2 = 98

123 x 8 + 3 = 987

1234 x 8 + 4 = 9876

12345 x 8 + 5 = 98765

123456 x 8 + 6 = 987654

1234567 x 8 + 7 = 9876543

12345678 x 8 + 8 = 98765432

123456789 x 8 + 9 = 987654321

1 x 9 + 2 = 11

12 x 9 + 3 = 111

123 x 9 + 4 = 1111

1234 x 9 + 5 = 11111

12345 x 9 + 6 = 111111

123456 x 9 + 7 = 1111111

1234567 x 9 + 8 = 11111111

12345678 x 9 + 9 = 111111111

123456789 x 9 +10= 1111111111

9 x 9 + 7 = 88

98 x 9 + 6 = 888

987 x 9 + 5 = 8888

9876 x 9 + 4 = 88888

98765 x 9 + 3 = 888888

987654 x 9 + 2 = 8888888

9876543 x 9 + 1 = 88888888

98765432 x 9 + 0 = 888888888

And look at this symmetry :

1 x 1 = 1

11 x 11 = 121

111 x 111 = 12321

1111 x 1111 = 1234321

11111 x 11111 = 123454321

111111 x 111111 = 12345654321

1111111 x 1111111 = 1234567654321

11111111 x 11111111 = 123456787654321

111111111 x 111111111 = 12345678987654321

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The Big Fat Model (Primary Math – Nanyang Primary 2016)

Frustrated with careless mistakes made when using the model method for solving problem sums in Singapore Primary School Math? Here’s the Big Fat Model for solving problem sums involving remainder concepts.

Ms Teo Lay Leng, a former MOE teacher and HOD created this method to help students understand model drawing questions better. Many of her students have found this to be an easier and less error-prone way to solve complex problem sums involving remainder concepts.

Here is a youtube video of a difficult problem sum listed below.

Question

And here is the step-by-step solution below.

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