All whole numbers boil down to 9
A whole number is a number without any decimal places., or expressed in fraction.
9 has a very special characteristic. If you follow the steps given below, the final answer will be 9.
The result or answer of adding two or more numbers or terms is known as Sum. The result or answer of subtracting one number from another is known as Difference.
METHOD
Step 1. Use any number greater than 9, that is, a number that has more than 1 digit
Step 2. Add the digit values together
Step 3. Subtract the Sum resulted in Step 2 from the original number
Step 4. Repeat steps 2 and 3 until the final Difference is left with 1 digit
Example
Step 1. Consider a number greater than 9, say 65
Step 2, 6 + 5 = 11
Step 3, 65 - 11 = 54
Repeat Step 2, 5 + 4 = 9
Repeat Step 3, 54 - 9 = 45
Repeat Step 2, 4 + 5 = 9
Repeat Step 3, 45 - 9 = 36
Repeat Step 2, 3 + 6 = 9
Repeat Step 3, 36 - 9 = 27
Repeat Step 2, 2 + 7 = 9
Repeat Step 3, 27 - 9 = 18
Repeat Step 2, 1 + 8 = 9
Repeat Step 3, 18 - 9 = 9
The final answer is 9.
It does not matter what the whole number is, as long as it is greater than 9, the final answer always finishes as 9 of the proper steps are followed.
Showing posts with label The Beauty of 9. Show all posts
Showing posts with label The Beauty of 9. Show all posts
Sunday, 26 April 2020
Divisibility by 9
Divisibility by 9
A number is divisible by 9, if the sum of the digits is divisible by 9
METHOD
Step 1. Add up the digits of the given number
Step 2. If the sum is divisible by 9, then the number is also divisible by 9.
Example 1. Consider the number 378
Step 1. 3 + 7 + 8 = 18
Step 2. 18 / 9 = 2
Since the sum of the digits is divisible by 9, so 378 is also divisible by 9.
Check. 378 / 9 = 42
Example 2. Consider the number 427
Step 1. 4 + 2 + 7 = 13
Step 2. 13 / 9= 1 remain 4
Since the sum of the digits is not divisible by 9, so 427 is also not divisible by 9.
Check. 427 / 9 = 47 remain 4
Example 3. Consider the number 8253
Step 1. 8 + 2 + 5 + 3 = 18
Step 2. 18 / 9 = 2
Since the sum of the digits is divisible by 9, so 8253 is also divisible by 9.
Check. 8253 / 9 = 917
Example 4. Consider the number 20872
Step 1. 2 + 0 + 8 + 7 + 2 = 19
Step 2. 19 / 9= 2 remain 1
Since the sum of the digits is not divisible by 9, so 20872 is also not divisible by 9.
Check. 20872 / 9 = 2319 remain 1
A number is divisible by 9, if the sum of the digits is divisible by 9
METHOD
Step 1. Add up the digits of the given number
Step 2. If the sum is divisible by 9, then the number is also divisible by 9.
Example 1. Consider the number 378
Step 1. 3 + 7 + 8 = 18
Step 2. 18 / 9 = 2
Since the sum of the digits is divisible by 9, so 378 is also divisible by 9.
Check. 378 / 9 = 42
Example 2. Consider the number 427
Step 1. 4 + 2 + 7 = 13
Step 2. 13 / 9= 1 remain 4
Since the sum of the digits is not divisible by 9, so 427 is also not divisible by 9.
Check. 427 / 9 = 47 remain 4
Example 3. Consider the number 8253
Step 1. 8 + 2 + 5 + 3 = 18
Step 2. 18 / 9 = 2
Since the sum of the digits is divisible by 9, so 8253 is also divisible by 9.
Check. 8253 / 9 = 917
Example 4. Consider the number 20872
Step 1. 2 + 0 + 8 + 7 + 2 = 19
Step 2. 19 / 9= 2 remain 1
Since the sum of the digits is not divisible by 9, so 20872 is also not divisible by 9.
Check. 20872 / 9 = 2319 remain 1
| Number | Step 1 | Step 2 | Step 2 Divisible by 9? | Number Divisible by 9? |
|---|---|---|---|---|
| 378 | 3 + 7 + 8 = 18 | 18 / 9 = 2 exactly | Yes | Yes |
| 427 | 4 + 2 + 7 = 13 | 13 / 9 = 1 remain 4 | No | No |
| 8253 | 8 + 2 + 5 + 3 = 18 | 18 / 9 = 2 exactly | Yes | Yes |
| 20872 | 2 + 0 + 8 + 7 + 2 = 19 | 19 / 9 = 2 remain 1 | No | No |
Saturday, 25 April 2020
Multiply any whole number between 1 and 10 by 9
Multiply any whole number between 1 and 10 by 9
In multiplication the numbers you multiply are called factors, the answer of multiplication is called the Product.
The product of multiplying a number between 1 and 10 by 9 has no more than 2 digits.
Let's call the two numbers used in the multiplication as Factor 1 and Factor 2, the number between 1 and 10 as Factor 1, and the 9 Factor 2. Factor 1 is also known as Multiplicand, and Factor 2 Multiplier.
METHOD
Step 1. Multiply a number between 1 and 10 by 9
Step 2. First digit of product equals to value of Factor 1 minus 1
Step 3. Second digit of product equals to Factor 2 minus the number obtained in Step 2
Step 4. Combine the numbers in Step 2 and Step 3 together to form the answer.
In multiplication the numbers you multiply are called factors, the answer of multiplication is called the Product.
The product of multiplying a number between 1 and 10 by 9 has no more than 2 digits.
Let's call the two numbers used in the multiplication as Factor 1 and Factor 2, the number between 1 and 10 as Factor 1, and the 9 Factor 2. Factor 1 is also known as Multiplicand, and Factor 2 Multiplier.
METHOD
Step 1. Multiply a number between 1 and 10 by 9
Step 2. First digit of product equals to value of Factor 1 minus 1
Step 3. Second digit of product equals to Factor 2 minus the number obtained in Step 2
Step 4. Combine the numbers in Step 2 and Step 3 together to form the answer.
| Step 1 | Step 2 | Step 3 | Step 4 |
|---|---|---|---|
| 1 x 9 | 1 - 1 = 0 | 9 - 0 = 9 | 09 or 9 |
| 2 x 9 | 2 - 1 = 1 | 9 - 1 = 8 | 18 |
| 3 x 9 | 3 - 1 = 2 | 9 - 2 = 7 | 27 |
| 4 x 9 | 4 - 1 = 3 | 9 - 3 = 6 | 36 |
| 5 x 9 | 5 - 1 = 4 | 9 - 4 = 5 | 45 |
| 6 x 9 | 6 - 1 = 5 | 9 - 5 = 4 | 54 |
| 7 x 9 | 7 - 1 = 6 | 9 - 6 = 3 | 64 |
| 8 x 9 | 8 - 1 = 7 | 9 - 7 = 2 | 72 |
| 9 x 9 | 9 - 1 = 8 | 9 - 8 = 1 | 81 |
| 10 x 9 | 10 - 1 = 9 | 9 - 9 = 0 | 90 |
Friday, 24 April 2020
Multiply any whole number by 9
Multiply any whole number by 9
METHOD
Step 1. Multiply the original number (Multiplicand) by 10, or just add one zero (0) at the right-hand end of the number
Step 2. Subtract the original number or Multiplicand from the new number worked out in Step 1
Step 3. The difference is the answer.
Example 1. Consider 5 x 9
Step 1. 5 x 10 = 50 or 50
Step 2. 50 - 5
Step 3. Answer 45
Example 2. Consider 67 x 9
Step 1. 67 x 10 = 670 or 670
Step 2. 670 - 67
Step 3. Answer 603
Example 3. Consider 4813 x 9
Step 1. 4813 x 10 = 48130 or 48130
Step 2. 48130 - 4813
Step 3. Answer 43317
METHOD
Step 1. Multiply the original number (Multiplicand) by 10, or just add one zero (0) at the right-hand end of the number
Step 2. Subtract the original number or Multiplicand from the new number worked out in Step 1
Step 3. The difference is the answer.
Example 1. Consider 5 x 9
Step 1. 5 x 10 = 50 or 50
Step 2. 50 - 5
Step 3. Answer 45
Example 2. Consider 67 x 9
Step 1. 67 x 10 = 670 or 670
Step 2. 670 - 67
Step 3. Answer 603
Example 3. Consider 4813 x 9
Step 1. 4813 x 10 = 48130 or 48130
Step 2. 48130 - 4813
Step 3. Answer 43317
| Number | Step 1 | Step 2 | Step 3 |
|---|---|---|---|
| 5 | 5 x 10 = 50 or 50 | 50 - 5 = 45 | 45 |
| 67 | 67 x 10 = 670 or 670 | 670 - 67 = 603 | 603 |
| 4813 | 4813 x 10 = 48130 or 48130 | 48130 - 4813 = 43317 | 43317 |
Multiply any whole number by a number consists of 9's only
Multiply any whole number by a number consists of 9's only
METHOD
Step 1. Add the same number of zeroes as the number of 9s in the second number (Multiplier) to the right-hand end of the first number or original number (Multiplicand)
Step 2. Subtract the original number or Multiplicand from the new number worked out in Step 1
Step 3. The difference is the answer
Example 1. Consider 5 x 9
Step 1. 9 has 1 digit, add only 1 zero (0) to 5 giving 50
Step 2. 50 - 5
Step 3. Answer 45
Example 2. Consider 67 x 99
Step 1. 99 has 2 digits, add 2 zeroes (00) to 67 giving 6700
Step 2. 6700 - 67
Step 3. Answer 6633
Example 3. Consider 481 x 999
Step 1. 999 has 3 digits, add 3 zeroes (000) to 481 giving 48100
Step 2. 481000 - 481
Step 3. Answer 480519
Example 4. Consider 123 x 9999
Step 1. 9999 has 4 digits, add 4 zeroes (0000) to 123 giving 1230000
Step 2. 1230000 - 123
Step 3. Answer 1229877
Example 5. Consider 726521 x 99999
Step 1. 99999 has 5 digits, add 5 zeroes (00000) to 726521 giving 72652100000
Step 2. 726521000000 - 726521
Step 3. Answer 7265127348
METHOD
Step 1. Add the same number of zeroes as the number of 9s in the second number (Multiplier) to the right-hand end of the first number or original number (Multiplicand)
Step 2. Subtract the original number or Multiplicand from the new number worked out in Step 1
Step 3. The difference is the answer
Example 1. Consider 5 x 9
Step 1. 9 has 1 digit, add only 1 zero (0) to 5 giving 50
Step 2. 50 - 5
Step 3. Answer 45
Example 2. Consider 67 x 99
Step 1. 99 has 2 digits, add 2 zeroes (00) to 67 giving 6700
Step 2. 6700 - 67
Step 3. Answer 6633
Example 3. Consider 481 x 999
Step 1. 999 has 3 digits, add 3 zeroes (000) to 481 giving 48100
Step 2. 481000 - 481
Step 3. Answer 480519
Example 4. Consider 123 x 9999
Step 1. 9999 has 4 digits, add 4 zeroes (0000) to 123 giving 1230000
Step 2. 1230000 - 123
Step 3. Answer 1229877
Example 5. Consider 726521 x 99999
Step 1. 99999 has 5 digits, add 5 zeroes (00000) to 726521 giving 72652100000
Step 2. 726521000000 - 726521
Step 3. Answer 7265127348
| Multiplicand | Multiplier | Number of 9's | Step 1 | Step 2 | Step 3 |
|---|---|---|---|---|---|
| 5 | 9 | 1 | 50 | 50 - 5 = 495 | 495 |
| 67 | 99 | 2 | 6700 | 6700 - 67 = 6633 | 663 |
| 481 | 999 | 3 | 481000 | 481000 - 481 = 480519 | 480519 |
| 123 | 9999 | 4 | 1230000 | 1230000 - 123 = 1229877 | 1229877 |
| 726521 | 99999 | 5 | 72652100000 | 72652100000 - 726521 = 7265127348 | 7265127348 |
Multiply any whole number by 99
Multiply any whole number by 99
METHOD
Step 1. Multiply the original number (Multiplicand) by 100, or just add two zeroes (00) at the right-hand end of the number
Step 2. Subtract the original number or Multiplicand from the new number worked out in Step 1
Step 3. The difference is the answer.
Example 1. Consider 5 x 99
Step 1. 5 x 100 = 500 or 500
Step 2. 500 - 5
Step 3. Answer 495
Example 2. Consider 67 x 99
Step 1. 67 x 100 = 6700 or 6700
Step 2. 6700 - 67
Step 3. Answer 6633
Example 3. Consider 4813 x 99
Step 1. 4813 x 100 = 481300 or 481300
Step 2. 481300 - 4813
Step 3. Answer 476487
METHOD
Step 1. Multiply the original number (Multiplicand) by 100, or just add two zeroes (00) at the right-hand end of the number
Step 2. Subtract the original number or Multiplicand from the new number worked out in Step 1
Step 3. The difference is the answer.
Example 1. Consider 5 x 99
Step 1. 5 x 100 = 500 or 500
Step 2. 500 - 5
Step 3. Answer 495
Example 2. Consider 67 x 99
Step 1. 67 x 100 = 6700 or 6700
Step 2. 6700 - 67
Step 3. Answer 6633
Example 3. Consider 4813 x 99
Step 1. 4813 x 100 = 481300 or 481300
Step 2. 481300 - 4813
Step 3. Answer 476487
| Number | Step 1 | Step 2 | Step 3 |
|---|---|---|---|
| 5 | 5 x 100 = 500 or 500 | 500 - 5 = 495 | 495 |
| 67 | 67 x 100 = 6700 or 6700 | 6700 - 67 = 6633 | 663 |
| 4813 | 4813 x 100 = 481300 or 481300 | 481300 - 4813 = 476487 | 43317 |
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