The Magic of Numbers in Mathematical Formulas

Magic Number 9

The privileges or magic of the number 9 include: Multiplying consecutive numbers and adding them 1 x 9 + 1 = 10 12 x 9 + 2 = 110 123 x 9 + 3 = 1110 1234 x 9 + 4 = 11110

Formula: 1234…n (and so on sequentially) x 9 + n = 1n (sum of sequence) 0

Multiply a positive integer 1-10 by 9 If a is a positive integer and it is multiplied by 9, the result is mn. Two numbers m and n when added together, the result is 9 (m + n = 9) Example: 1 x 9 = 9 2 x 9 = 18 1 + 8 = 9 3 x 9 = 27 2 + 7 = 9 4 x 9 = 36 3 + 6 = 9 5 x 9 = 45 4 + 5 = 9 6 x 9 = 54 5 + 4 = 9 7 x 9 = 63 6 + 3 = 9 8 x 9 = 72 7 + 2 = 9 9 x 9 = 81 8 + 1 = 9 10 x 9 = 90 9 + 0 = 9

Addendum: Multiply by 9 can be found without calculating manually or using calculators. If the result of multiplying an integer 1-10 by 9 is mn, then the number mn can be determined in the following way: m goes down, increases 1 digit (integer 1-10 multiplied by 9, for example 2 x 9 = 18 ; 3 x 9 = 27 and so on up to 10). n goes down, decreases by 1 number (integers 1-10 multiplied by 9, for example 2 x 9 = 18 ; 3 x 9 = 27 and so on until 10)

Multiplication of integers > 10 by 9 Similar to multiplication of integers 1-10, for positive integers > 10 also has a magical result, that is, if the numbers are added up, the final result will be 9. Example: 11 x 9 = 99 9 + 9 = 18 1 + 8 = 9 87 x 9 = 783 7 + 8 + 3 = 18 1 + 8 = 9

Multiply the number of doubles by 9 22 x 9 = 198 55 x 9 = 495 88 x 9 = 792 99 x 9 = 891

Look at the multiplication above, the number 9 always appears in the middle. The formula to quickly calculate the multiplication of doubles by 9: Example: 33 x 9 (3 obtained from the multiplication of twins, which is 33) 3 x 9 = 27, then insert the number 9 in the middle so 297 results from the multiplication of 33 x 9

Multiplication of twins 3 by 9 To find out the result of multiplying the number of twins 3 by 9, it is the same as multiplying the number of twins 2 by 9. The difference is that we just insert 2 numbers in the middle. Formula: the same as in point D 333 x 9 3 x 9 = 27 Insert the nine in the middle (two numbers because of the triple multiplication of 3). The result is 2997

Multiplication of twins by 4 – infinite twins by 9

To find out the result of multiplication of twins 4 to infinite twins with 9 is in the same way as multiplication of twins in the previous points. That is how to multiply one number, then insert the number 9 as many as the twin numbers minus 1 (see points D and E) Example: 7777 x 9

7 x 9 = 63 because the number that has twins is 4, it means it is reduced from 1 to 3 then insert 3 9s in the middle. The result is 69993 444444 x 9

4 x 9 = 36 because the number that there are twins is 6 means it is reduced from 1 to 5 then insert 5 numbers 9 in the middle. The result is 3999996.

The Mystery of the Number 123 in Mathematics

With a certain calculation method we will always get the final result 123. So this mystery is also known as the mystery number 123, there are also those who call it a mathematical blackhole (blackhole in mathematics). To prove the calculation method is as follows:

1. Now try to take a paper and write down any number from 1 digit to infinity

2. For example in this paper, the number taken is 158,261

3. Then count the number of even numbers, odd numbers, and the total number of these numbers. In this case we will get: 3 digit even number (8, 2, 6) 3 digit odd number (number 1, 5, 1) 6 digit total of the whole number

4. Next take and combine each number of digits above as a new digit. Then you will get the number 336

5. The next step is to repeat step no.3 above, which is to count the number of even, odd numbers, and the total number of the result is 123. Additional: If the result is not yet 123, then repeat step no.3 on a large number of numbers, sometimes 3 repetitions are required.

Magic Number 6

1 + 2 + 3 + 4 + 5 + 6 = 21 1 + 2 + 3 + 4 + 5 + 6 + … + 66 = 2211 1 + 2 + 3 + 4 + 5 + 6 + … + 666 = 222111 1 + 2 + 3 + 4 + 5 + 6 + … + 6666 = 22221111

Take a look at the sum of the results above, the results of the sum are in accordance with the number of the last addition. For example 1 + 2 + 3 + 4 + 5 + 6 + … + 6666 = 22221111 because the final sum is 6666 (number 6 is repeated up to 4 times) then the result is 22221111 (numbers 2 and 1 are also repeated up to 4 times)

Magic Number 11

Pyramid of the number 11

1 x 1 = 1 11 x 11 = 121 111 x 111 = 12321 1111 x 1111 = 1234321 11111 x 11111 = 123454321 111111 x 111111 = 12345654321 11111111 x 11111111 = 1234567654321 11111111 x 11111111 = 123456787654321 11154111111 x 11176111 = 123456789811111 always sequential Example: 11 x 11 = 121 Always the number 1 which is located in front and behind and the repetition starts from the number whose number is the same as the number of digits 1 on the left side. In multiplication of numbers 11 (eleven) also has a unique and faster way to find out the result. Example: 11 x 11 1 .. 1 = 1 + 1 = 2 The number 2 is inserted in the middle so that the result is 121 And always use the same way to do the multiplication of 11 against a factor of three decimal places, four decimal places and so on.

Those are some of the magic of numbers in the world of mathematics, which maybe not many people know about, sharing knowledge is very beautiful.