Hello steemians, it's been a while since I made my last post. I’ve been busy with work and some other things. My last article was about the most beautiful mathematical equation in the world and I hope to show you how to derive the equation in my next post. Nevertheless, I’d love to share with you guys a cool maths trick.
Don’t you wish you could perform multiplication operations without the need for a calculator or using the long and boring method to multiply numbers. Well, in this article, I would be showing you a shortcut to multiplying any number by 9. Cool huh? There are about two different ways to go about it and I’ll be showing you both methods here.

Method 1

You might have come across this method of multiplying a number by 9. Let me just get to it, so as not to bore you with my talk.
Let's pick a number say 15

Step 1

You can get the solution by multiplying 15 by 10 (multiplication with 10 is very easy, zero is added to the number).
15 * 10 = 150

Step 2

The next step is to subtract the number (15 in this case) from the result above. Thus, we have
150 * 15= 135
Thus, 9 * 15 = 135.

Let's try another example.
This time let us pick the number 33

Step 1

33 * 10 = 330

Step 2

330 * 33 = 297.
So 9 * 33 would give 297
Let's go even further and pick a 3 digits number
Let's pick 321

Step 1

321 * 10 = 3210

Step 2

3210 * 321 = 2889.
You see its very easy.
Let's move to the second method.

Method 2

This method is a bit tricky and not as easy as the first method.
Let me start by showing you the 9 multiplication table.
9 * 01 = 09
9 * 02 = 18
9 * 03 = 27
9 * 04 = 36
9 * 05 = 45
9 * 06 = 54
9 * 07 = 63
9 * 08 = 72
9 * 09 = 81
9 * 10 = 90
9 * 11 = 99
9 * 12 = 108

I actually stumbled upon this trick while looking at the multiplication table. If you can notice, the last digit from each of the answers is the zero compliment if the last digit of the number multiplying 9 (that is the sum of the last digits of the number multiplying 9 and the answer gives a ten).
For 9 * 12 = 108 we have 2 + 8 = 10
9 * 3 = 27 we have 3 + 7 = 10
You can see that it applies to all the numbers, the sum of last digits will always give a 10 (you can check) . Note that the zero compliment if 0 is 10. Let’s get started with the steps.
Let’s start by multiplying the number 15

Step 1

Remove the last digit from the number
We have just 1

Step 2

Add 1 to the result from step 1
1 + 1 = 2

Step 3

Subtract the result you got in step 2 from the original number (15)
15 – 2 = 13

Step 4

Place the zero compliment of the last digit in front of the answer in ** step 3 ** (this is equivalent to multiplying the answer from ** step 3 ** by ten and adding the zero compliment of the last digit).
Zero compliment of 5 = 5
135
Therefore, 9 * 15 = 135
This method is actually easier than it looks. It’s the explanation that make it look long and boring.

Let’s try another number 33

Step 1

Remove the last digit from the number
We have just 3

Step 2

Add 1 to the result from step 1
3 + 1 = 4

Step 3

Subtract the result you got in step 2 from the original number (15)
33 – 4 = 29

Step 4

Place the zero compliment of the last digit in front of the answer in ** step 3 ** (this is equivalent to multiplying the answer from ** step 3 ** by ten and adding the zero compliment of the last digit).
Zero compliment of 3 = 7
135
Therefore, 9 * 33 = 297

Let’s try another example this time the number should end with a zero, say 60

Step 1

Remove the last digit from the number
We have just 6

Step 2

Add 1 to the result from step 1
6 + 1 = 7

Step 3

Subtract the result you got in step 2 from the original number (15)
60 – 7 = 53

Step 4

Place the zero compliment of the last digit in front of the answer in ** step 3 ** (this is equivalent to multiplying the answer from ** step 3 ** by ten and adding the zero compliment of the last digit).
Zero compliment of 0 = 10
53 *10 + 10 = 530 + 10 = 540
Therefore, 9 * 60 = 540

Let’s go even further to try a 3 digit number, say 321

Step 1

Remove the last digit from the number
We have just 32

Step 2

Add 1 to the result from step 1
32 + 1 = 33

Step 3

Subtract the result you got in step 2 from the original number (15)
321 – 33 = 288

Step 4

Place the zero compliment of the last digit in front of the answer in ** step 3 ** (this is equivalent to multiplying the answer from ** step 3 ** by ten and adding the zero compliment of the last digit).
Zero compliment of 1 = 9
2889
Therefore, 9 * 321 = 2889
Before I forget, it’ll be highly unprofessional of me not to show you the mathematics behind this trick.
Suppose we have a number [XY] (this is not a multiplication operation) where Y is the last digit (can only contain one digit) and X is the other digits (every other number without the last digit). We can write the number [XY] as.
[XY] = 10X + Y
9 * [XY] = 9 * [10X + Y]
= 90X + 9Y

Following the steps I gave

Step 1

Remove the last digit from the number
We have just X

Step 2

Add 1 to the result from step 1
X + 1 = X + 1

Step 3

Subtract the result you got in step 2 from the original number ([XY])
[XY] – (X + 1) = (10X + Y) - (X+1)
= 10X + Y -X – 1
= 9X + Y – 1

Step 4

Place the zero compliment of the last digit in front of the answer in ** step 3 ** (this is equivalent to multiplying the answer from ** step 3 ** by ten and adding the zero compliment of the last digit).
Zero compliment of Y = 10 - Y
(9X + Y – 1) * 10 + (10 – Y)
Simplifying,
90X + 10Y – 10 + 10 – Y
90X + 9Y
This shows the mathematics behind the trick. I hope you understand the trick and its proof ( I ain’t that good at explaining stuffs). Tell me in the comment section , if you understand this trick and what you think of it.