Easy Multiplication trick for BIG numbers.

This trick for multiplication is awesome! Multiply numbers near 100 in under 5 seconds. Remember - you don't need a clickbait title to view this - you are far far better than that! Five minutes - you havre another multiplication math trick up your sleeve!

Here is THE mental multiplication lesson playlist - progressing you through your mental multiplication.

[brickmason]

My 8th grade teacher taught me this, he said we would need to use this all our lives.

[JAUNEtheLOCKE]

I recently turned 20 and I’m in the process of taking ENEM (big national test here in Brazil to get into university) and these kinds of videos are a BIG help because it helps me finish “medium” questions faster so that way I’ll have more time for the other math questions. Thank you so much! ❤

[erinmalone]

It has been many moons since I’ve done any math. Really glad they have these refreshers and tricks. Never stop learning and reviewing.

[traceycole]

Man you are a gifted math teacher.. wish all teachers taught this in the 1970's

[TON-vzpe]

As others said, this works well if both your numbers are close enough to base 10 numbers. Also, this will work only with few special combinations, where both the multipliers are having a additive/substractive relationship.

[kingrobbo]

You continue to amaze me. I have been watching and learning for a long time now and I will be teaching my kids when they are of age. I'm sure they will enjoy maths a lot more than I did.

[angelicaannegreen]

I wish videos like this were available in the 1980s. Thank you for creating this channel. This is great for my kids who love maths. I am a lifelong student who loves to learn new and better ways of doing things. Great students are created by capable and engaging teachers.

[IS-pydk]

Well i am sitting in classes and this video just got released before my Math Lesson 😃😃😂😂

[seniorsabali]

Damn I'm blown away watching this as an adult and I wish I had this channel when I was a kid. Loving it

[mohamedyazar]

Maths was the most sweetest subject for me in the school. No calculators no devices but we were all doing pretty good. If I knew this trick 25 years ago I could be the king of class !!!

[nonaknight]

🇬🇧IF👀 only I had been taught this 70+ years ago when I was good art & enjoyed maths!. . Don’t get OLD🤬🇬🇧

[yonatanshenhav]

Tecmath, you sound roughly my age, and i want to tell you i've searched the internet for a channel like this for many years (i love calculating). So thank you so much for devoting the time and helping me.

[paulothx]

Those math tricks are amazing, thank you, sir.

[fengjiaozhang]

How do people even find so many shortcuts？

[guygod]

Anytime I have a math presentation due in school but don't know what to do, I just come here. Never disappoints!

[yasaine]

How much thought you put in these lessons are incredible! Very appreciate it

[scmtuk]

When you look at these methods in a more general algebraic way, it actually shows how this works.

In this case, we're treating each number as 100+a and 100+b respectively.

So the multiplication becomes (100+a)(100+b)

Then what we're doing is we are adding one of the numbers to the difference from 100 for the other number.
I.e. (100+a)+b or (100+b)+a. This will be the first 2 digits, and therefore, will be multiplied by 100, to get 100(100+a+b) or 10000+100(a+b)
Then next part is to simply multiply the differences, i.e. ab. Therefore, (100+a)(100+b) = 10000+100(a+b)+ab
And if you simply "expand" (100+a)(100+b) you will get the same answer of 10000+100(a+b)+ab.

And yes, this works with decimals.
For example what is 99.6 x 102.5?

In this case, a = -0.4 and b = 2.5

So, we take either 99.6+2.5 = 102.1, or 102.5-0.4 = 102.1

Then we multiply the -0.4 by 2.5 to get -1

So, how does this work? First, we have 102.1 for the first part of our answer. This will be a multiple of 100, so we'll treat this as 10210.
Then we simply add the -1 (i.e. we subtract 1) to get 10209.

And, yes, you can use this method for really easy multiplications. However, the easier the multiplication, the harder the method.

For example, take 2 x 3.

That's a difference of -98 and -97 respectively.
So, we apply the same logic.
2-97 = -95 (or 3-98 = -95)

We then have -9500 as the first part of our answer. Yes, the answer will be negative at this point.
Then we simply multiply -97 x -98, which is the same as 97 x 98 (which we can then do, using the same method):
97 x 98 is -3 and -2 respectively. 97-2 = 98-3 = 95, so the first part of _this_ answer is 9500.
Then -2 x -3 = 6, so 97 x 98 = 9506.
Now, we can add this 9506 to the -9500 earlier, to get 6.
And so, we have discovered that 2 x 3 = 6. It's so simple.

Of course, this method can also apply similarly to any power of 10. There are just some extra steps for every power of 10 you go up.

For numbers that are near 10, it's even easier.

For example 8 x 12. We use the same principal, of finding how far each number is from 10, in this case, they are -2 and 2 respectively.

So we have 8+2 or 12-2 respectively to get 10. We then multiply this 10 by 10 to get 100.
Then we multiply the 2x-2 to get -4. Then add 100+-4 to get 96.

And the same can apply to 1000 and 10000 etc.
Take 995 x 992. This is -5 and -8 from 1000 respectively.

Then simply do the same method.
995-8 or 992-5 to get 987
Multiply this by 10000 to get 987000.
Then -8 x -5 = 40. Add this to 987000 to get 987040.

Infact, this doesn't actually need to apply to just 10, 100, 1000, 10000 etc. You can do the same with multiples of this power. However, there's just a small change.

For example, let's take 28 x 35, and work out the difference from each number to 30.

28 is -2 from 30, and 35 is 5 from 30.

Add the difference from one number to the other number, i.e. 28+5 or 35-2 to get 33.
Now, because this is 30, we need to multiply the number by 30 to get 990.
Then we just multiply the differences together, i.e. 5 x -2 = -10. Then subtract 10 from 990 to get 29690.

Infact, the general idea, is that we find the distance from _any number_ .... then add either number to the difference from the other number to get the first part of our answer, and then multiply this part with the number from which we were finding the difference from.
Then the last part is always the same, i.e. multiplying the diffences.

The reason this always works is this.

If we take two numbers to be represented by a fixed number, plus or minus any variable, i.e. (a+b)(a+c), we can look at it algebraically:
Adding one number to the difference to the other number gives us (a+b)+c or (a+c)+b which are both obviously the same.
Then we're multiplying this number by a itself, so we get a(a+b+c) which can be expanded as a²+ab+ac
Then we simply add the product of the two differences, i.e. bc to get a²+ab+ac+bc, which is also what happens if we expand (a+b)(a+c)

[hackerone]

The explanation of the first example ( you can also use to prove the other ones):

89 x 94 = ( 100 - 11 ) x ( 100 - 6 ) =
100 x 100 - 100 x 6 - 11 x 100 + 11 * 6
100(100 - 6 - 11) + 66 = 8300 + 66


(100 - 6 - 11) this is the part that gives us how many hundreds we have ( 83 * 100 ) = 8300
And 11 * 6 remaining part.

[ypb]

why isn't this taught in school! Life/grade saving! 👍👏🤗

[clintonmanning]

That’s unbelievable lol. I have never heard of this method, now I can’t stop doing sums 😂