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! ❤
@@jackh577 I multiplied 43 x 30 + 43 x 2 and got the answer in less that 10 seconds. I was fortunate that I had the same teacher 2 years in a row and he taught algebra but made sure we learned math we would use constantly. He did the same thing with addition.
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.
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.
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.
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.
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.
@@tecmath oh oh, i sense a trap which im about to fall into. Well, youre not a woman so im allowed to be honest with my answer without insulting you (if you were a woman i'd say you sounded... 18 years old, and weighed 41 kg). So my final answer is you sound like the square root of 1936 years old
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)
@@vidtuby Yes, i found a way to shorten the working out of Calculas, and was marked down as the right answer, but no working out on paper, as I did it in my head. back in 1987.
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 !!!
Problems can be rewritten as (100+a)*(100+b) -- where a & b can be positive or negative. Distributing that, we get 100*100 + 100*a + 100*b + ab, or 100*(100+a+b) + ab. The sum in parentheses is what becomes those first two (or three) digits in his examples. That first 100 shifts that sum over two places to the left. And obviously, the ab is just the last two digits. So taking the first question as an example, 89*94. In this case we have a = -11 & b= -6. So: (100-11)*(100-6) = 100*(100-11-6) + (-11)*(-6) = 100*(100-17) +66 = 83*100 + 66 = 8366. It might be confusing that for the parentheses, I did 100-11-6 = 100-17, whereas he did 89-6. But remember that 89 is simply 100-11, so really the same thing. Many will probably find it easier to do it the way shown in video, since it's a little shorter, and less to "hold in your head". But personally, I find it easier to remember, and understand by doing it the way I showed: add the two differences to 100 (being careful with the signs!). Doing it that way allows me to apply the technique to a greater variety of numbers than can be done with the original "trick" as shown.
Dude your tricks are so usefull.... As soon as your new video comes out i leave all my work to see this... I am a student so your videos help me out a lot♥️♥️
This way of doing math has never been taught to me... I like how your way has opened my mind on seeing these equations differently. Awesome work my good sir.
@@oldcountryman2795 school taught me the right way?? Firstly, what does that even mean? If you get the right answer, then how is that wrong. Secondly, if I was shown how to do math the way this guy does, then I wouldn't have had to take pre-algebra 3 times in college just to move on from my pre-requisites! Bye!
@@oldcountryman2795 The multiplication way you're saying stupid to do multiplications, also has a reason for its working. It's also related to other mathematical identities. If you say these are stupid then don't use (a+b)^2=a^2+2ab+b^2. And then see. Everything has a reason to work, obviously. Schools are just not updated to the level of using these identities as easy multiplications, divisions, subtractions, and additions.
Thanks ur helping me a lot with math so when I finish my break that I’m on I can be even better I always thought I knew math fully and it was easy but ur teaching me struggle I’ve never seen
This is awesome. Just a short cut to F(irst)O(uter)I(nner)L(ast) Where both the FIRST numbers are 100. Thus the subtraction of the differences becomes the Outer and Inner. Then the multiplying of the differences becomes the last 97 91 8827 100 -3 100 -9 F 10000 O -900 This is the 91 (100 - 9) I -300 This is the 88 (91 - 3) L 27 These are the last (-9 * -3) 8827
I have just subscribed after watching this excellent tip. As a private tutor, I found this it to be a great help, especially as maths is my weakest subject. However, where it gets tricky is when the numbers are `not' so close to 100, such as 79 x 53 = 4187?
Let's say the numbers are (100+a) and (100+b) Now, (100+a)(100+b) =10000+100a+100b+ab =[100(100+a+b)]+[ab] Here this one is more of a general format, similar to the case if both numbers are greater than 100, if either 'a' or 'b' or both are negative, we can simply put it with a negative sign, and it will lead to the shortcut eventually.. This one is such a cool and beautiful trick, children should be taught about this one, these are fun parts of mathematics..and also when you'd do the calculation to crosscheck, and the answer comes out to be exactly same..it just feels so good man!
What is the need of Mathematics? To gain marks in the exam? To sharpen the brain? To measure many things? If there's a best thing about Mathematics, then it is to discover the space mathematically. Scientists found Black holes mathematically in the earlier 20th century and now NASA took a photo of Black hole in 2019. They also found a Black hole pulling a star into itself, which was stated earlier that Black holes pull objects into themselves.
So how would 20x20 work? Doing this math I see 1st step is to do 100 and subtract 20 which = 80 (or -80 to be consistent with the method shown in video). So now we take the other 20 (just ironic there's two 20's) and subtract that 80. We get -60. 20x20 = 400, so I figure there must be an alternate step or method to calculate such a problem as 20x20? Love the videos! Great fun math shortcuts I never seen or heard about. Thanks for sharing!
2 digits numbers that both end in 0 is stupid easy, just take the zeros away, multiply, and then add them back. 60 * 60 is 6*6, which is 36, put the 0s back, 3600. It even works for big numbers, albeit not as easy. 4,800*4,800=48*48, which is 2,304, put the 0s back, answer is 23,040,000. This video's method is only for numbers really close to 100, too high or low and it falls apart.
No. It's a special case where math rules allow simplification to pose as a trick. The base formula here is: `(X + a)(X + b)` which evaluates to `X² + aX + bX + ab` In this special case we use X=100, so if you take the initial example of 89 x 94 you can rewrite this as `(100 - 11)(100 - 6)` and evaluate to `(100 x 100) - (11 x 100) - (6 x 100) + (6 x 11)` which contains three elements that multiply by 100 (i.e. X). The trick follows when you group these three elements to become `(100 - 11 - 6) x 100 + (6 x 11)`, or as the trick is explained `(89 - 6) x 100 + (6 x 11)`
i think this channel talks about maths too advanced for me (im in year 6 - well almost) but im one the smartest in my class and can do basic algebra (example: 5Ｘ+3÷8=6) so yea! and thanks for helping and using up your time so generously to help
