I also know a trick: If there is 2 x 5 between any multiplication then you can forget it and put a 0 For example : 2 x 6 x 9 x 5 Usually we multiply 2 with 6 and get 12 and then multiply 12 with 9 and then the answer with 5. But you can forget the 2 and 5 and multiply 6 with 9. The answer is 54. And the 2 and 5 become 0. You add the 0 after 54. So the answer is 540. In this way you can do maths very fast.
Awesome! And that about the cost of gas, you can even take it one step further and add the remaining 0.42 which you calculate from 14x0.03, so just use that mind trick, and then fix up the rest of the digits, amazing! Love it
1. Ignore the 5's. 2. Add the Product and Average of the leading digits. (Product+Average) 3. Multipy the resultant by 100. 4. Add 25. You will get the answer. Overall: ((Product+Avg)*100)+25 Note: - Product and Average of leading digits . Ignore the 5 in the whole process. Proof: (10x+5)(10y+5) 100xy+50(x+y)+25 100(xy+ (x+y)/2) + 25 ie. 100(PROD+AVG) + 25
The reason this works is pretty obvious. If we split the terms into (x+5)(y+5), we then get xy + 5x + 5y + 25. The 25 is added in the last step, so we'll ignore that. Also, x and y are both guaranteed to be divisible by 10, so we can use the trick for multiplying numbers divisible by 10, [(x/10)(y/10)]*100. Now we have 5x + 5y left. If we divide by 100, we get [(x/10)+(y/10)]/2. You'll notice that this is the average of x/10 and y/10. But now, we need to multiply that result by 100 to keep the end value the same. Putting that back into the expression, we get: [(x/10)(y/10)]*100 + [(x/10)+(y/10)]/2*100 + 25 Since x and y are both divisible by 10, dividing them by 10 is the same as cutting off the last digit, which is what was done in the video. Therefore, to make this clearer, we will replace x/10 with a and y/10 with b. 100ab + (a+b)/2*100 + 25 And if we condense it further, we get: 100[ab+(a+b)/2] + 25 Notice this is exactly what he did in the video. Get the product of the numbers with their last digits cut off, add it to their average, multiply it by 100 and add 25. FYI I didn't watch the rest of the video before writing this.
There's a (possibly) easier method using the difference of two squares identity: a^2 - b^2 = (a - b)(a + b). Let a be the average of the two numbers and b is half the difference between them. e.g. 15 x 35 = (25 - 10)(25 + 10) = 25^2 - 10^2 = 625 - 100 = 525 65 x 75 = 70^2 - 5^2 = 4900 - 25 = 4825 35 x 115 = 75^2 - 40^2 = 5625 - 1600 = 4025 18 x 46 = (32 -14)(32 + 14) = 32^2 - 14^2 = 1024 - 196 = 828 - tbh that one was a bit harder to work out in my head It works well for finding the squares of numbers too by flipping the formula: a^2 = (a - b)(a + b) + b^2. e.g 45^2 = (45 - 5)(45 + 5) + 5^2 = 40 x 50 +25 = 2025 97^2 = 100 x 94 + 9 = 9409
Using Basic Algebra, we can prove this: Since both the numbers are multiples of 5, they can be expressed as below : First Number= (10a+5) Second Number = (10b+5) Product of the two numbers : __________________________________________________ First Number * Second Number = (10a+5)*(10b+5) =100ab+50(a+b)+25 =100(ab +(a+b/2)) + 25 __________________________________________________ which means 100 multiplied by sum of product of the numbers and average of the two numbers.
+Bungis Albondigas No, there is no limit. The proof at the end shows this. Though, as you get more and more digits it will become harder and harder to multiply the leading digits.
I have my own super cheating thing that also about this 5-5 multiplication,the word form is long but it's easy to do: 1-Find the product of the smaller leading digit and (the total of the bigger leading digit and 1) 2-Multiply by 100 3-Add the (product of 50 and the difference of the leading digits) 4-Add 25 Example:75*165 7*(16+1)=7*17=119 119*100=11900 11900+50*(16-7=9)=12350 12350+25=12375 75*165=12375 If you don't believe it,then i move from the simple one: 15*15(same leading digits) 1*(1+1)=2 2*100=200 200+50*(1-1)=200 200+25=225 15*15=225 Or: 15*35=525(the bigger leading digit always plus 1 not the smaller one) 1*(3+1)=4 4*100=400 400+50*(3-1)=500 500+25=525 15*35=525 The result is:((SLD)*(BLD+1))*100+50*(BLD-SLD)+25 SLD=Smaller leading digit BLD=Bigger leading digit So,if you accidentally add 1 to the smaller leading digit,the result is wrong!: Example:35*15 3*(1+1)=6 6*100=600 600+50*(3-1)=700 700+25=725 But 35*15 is 525 not 725 so That's why you should always add 1 to the bigger leading digit ONLY if the multiplication has the different leading digits from each number!
Last step: take the difference between 18 and 15 cents, which is 3 cents, and multiply by 14. This gives you 42 cents which you add to the 44.10 for 44.52.
the easier way without multiplying by 100 and avoiding decimals 15 x 35 ------- 1 x 3 || 5 x 5 3 || 25 + 2 0 -----> add the average of 10 + 30 (20) and put just before the unit's place --------- = 525 65 x 75 ------- 6 x 7 || 5 x 5 42 || 25 + 6 5 ----> add the average of 60 + 70 (65) and put just before the unit's place ---------------- = 4875
An easier way to visualize this is to realize that if you were to divide a multiple of 5 by 10, it becomes adding a half. For example = 42 * 15 = 10 * 42 * 1.5 In the above example, you are multiplying by 1 and a half. So, mentally you could take 42 + 21 = 63 and multiply by 10, to get 630. However, this can be easily expanded by using any multiplication with multiples of 5. As simple as 54 * 5 = 270 (either by multiplying outright, or dividing by 2 and multiplying by 10). This video takes the same principle, essentially. 45 * 45 for example is the same as 10 * 45 * 4.5 So, you multiply 45 by 4 (as stated above) to get 180, add half of 45 (22.5) 202.5 and multiply by 10, to get 2025. Multiplication with 15 is also to think about when realizing, you can also divide by 2, and multiply by 3, and then by 10. 18 * 15 = 270 (divide 18 by 2, multiply by 3, and then multiply by 10). There are lots of cool tricks out there. I just had noticed the commonality with the (adding the average) as essentially being the same as what I've been doing for years with thinking of the 5 as a half of 10, and then adding that on.
Add non last digits (numbers ending with 5 only, lets call the numbers x and y frm here) and then if it odd the result ends with 75 else ends with 25. And now for the remaining Add take average of the x and y as in the video and ignore the decimal And add it to the multiplication result of x and y
Let's taks your example 65x75 When their difference is 10 then Write 75 in the left After that Multiply lower tens digit with higher tens digit plus 1 u will gwt the answer __75 6x8= 48
15555*15155= product : 1555*1515 = 2,355,825 average : (1555+1515)/2 = 3070/2 = 1,535 you add both product and average and you get : 2,357,360 you multiply by 100 to get : 235,736,000 and then you add 25 to get : 235,736,025
your "proof" makes no sense, you don't even explain why you did 50(x+y) you just did it thats confusing and then the last step of factoring out 100, where did the 50 go?! like explain don't just say nonsense without explanation
@@a-z5439 actually you add all the numbers and divide by the number of digits you added for ex: 5+4+3= 12 divided by 3=4 so 4 is the average of 5,4,3 ☺️
Shubhangi Chaturvedi I’m even more confused to be honest but thanks for trying, my main point is the title starts by saying easy method and I find nothing easy about any of the methods above
![I.N "HALLUCINATION" | [Stray Kids : SKZ-PLAYER]](http://i.ytimg.com/vi/n5B5q1Hwt_U/mqdefault.jpg)
I also know a trick:
If there is 2 x 5 between any multiplication then you can forget it and put a 0
For example : 2 x 6 x 9 x 5
Usually we multiply 2 with 6 and get 12 and then multiply 12 with 9 and then the answer with 5. But you can forget the 2 and 5 and multiply 6 with 9. The answer is 54. And the 2 and 5 become 0. You add the 0 after 54. So the answer is 540. In this way you can do maths very fast.
You have some extraordinary sarcasm right here (I hope so)
You sound so EXCITED in this video!
Sounds really forced to me
Awesome! And that about the cost of gas, you can even take it one step further and add the remaining 0.42 which you calculate from 14x0.03, so just use that mind trick, and then fix up the rest of the digits, amazing! Love it
*WooW...!*
14*0.03 do 14*3 = 42 and divide by 100
Difference in squares is useful here. Ex: 525 is 625(25 squared) minus 100(10 squared). 25 squared minus 10 squared =(25+10)(25-10) or 35x15=525.
Thats what I thought at first.. 25×55= 40 square 1600 minus 15 square 225= 1375
This seems a lot harder than just multiplying the fucking numbers.
1. Ignore the 5's.
2. Add the Product and Average of the leading digits. (Product+Average)
3. Multipy the resultant by 100.
4. Add 25. You will get the answer.
Overall:
((Product+Avg)*100)+25
Note: - Product and Average of leading digits .
Ignore the 5 in the whole process.
Proof:
(10x+5)(10y+5)
100xy+50(x+y)+25
100(xy+ (x+y)/2) + 25
ie.
100(PROD+AVG) + 25
The reason this works is pretty obvious. If we split the terms into (x+5)(y+5), we then get xy + 5x + 5y + 25. The 25 is added in the last step, so we'll ignore that. Also, x and y are both guaranteed to be divisible by 10, so we can use the trick for multiplying numbers divisible by 10, [(x/10)(y/10)]*100. Now we have 5x + 5y left. If we divide by 100, we get [(x/10)+(y/10)]/2. You'll notice that this is the average of x/10 and y/10. But now, we need to multiply that result by 100 to keep the end value the same. Putting that back into the expression, we get:
[(x/10)(y/10)]*100 + [(x/10)+(y/10)]/2*100 + 25
Since x and y are both divisible by 10, dividing them by 10 is the same as cutting off the last digit, which is what was done in the video. Therefore, to make this clearer, we will replace x/10 with a and y/10 with b.
100ab + (a+b)/2*100 + 25
And if we condense it further, we get:
100[ab+(a+b)/2] + 25
Notice this is exactly what he did in the video. Get the product of the numbers with their last digits cut off, add it to their average, multiply it by 100 and add 25. FYI I didn't watch the rest of the video before writing this.
He did it so much faster...
There's a (possibly) easier method using the difference of two squares identity: a^2 - b^2 = (a - b)(a + b).
Let a be the average of the two numbers and b is half the difference between them.
e.g. 15 x 35 = (25 - 10)(25 + 10) = 25^2 - 10^2 = 625 - 100 = 525
65 x 75 = 70^2 - 5^2 = 4900 - 25 = 4825
35 x 115 = 75^2 - 40^2 = 5625 - 1600 = 4025
18 x 46 = (32 -14)(32 + 14) = 32^2 - 14^2 = 1024 - 196 = 828 - tbh that one was a bit harder to work out in my head
It works well for finding the squares of numbers too by flipping the formula: a^2 = (a - b)(a + b) + b^2.
e.g 45^2 = (45 - 5)(45 + 5) + 5^2 = 40 x 50 +25 = 2025
97^2 = 100 x 94 + 9 = 9409
I thought I was the only one thinking like that..
Sounds interesting, but I'd like more details for 'average' calculation which I am not exactly clear about...
Using Basic Algebra, we can prove this:
Since both the numbers are multiples of 5, they can be expressed as below :
First Number= (10a+5)
Second Number = (10b+5)
Product of the two numbers :
__________________________________________________
First Number * Second Number = (10a+5)*(10b+5)
=100ab+50(a+b)+25
=100(ab +(a+b/2)) + 25
__________________________________________________
which means 100 multiplied by sum of product of the numbers and average of the two numbers.
Any limits to this? Does it break when the leading digits go over a certain count, or are a certain set?
+Bungis Albondigas No, there is no limit. The proof at the end shows this. Though, as you get more and more digits it will become harder and harder to multiply the leading digits.
SlimThrull Interesting. I wonder if there is a division trick to use like this in a similar way without limits...
Superb tricks
Calculating average takes lot more time
You learn something new every day... That's the beauty of math!!!
I have my own super cheating thing that also about this 5-5 multiplication,the word form is long but it's easy to do:
1-Find the product of the smaller leading digit and (the total of the bigger leading digit and 1)
2-Multiply by 100
3-Add the (product of 50 and the difference of the leading digits)
4-Add 25
Example:75*165
7*(16+1)=7*17=119
119*100=11900
11900+50*(16-7=9)=12350
12350+25=12375
75*165=12375
If you don't believe it,then i move from the simple one:
15*15(same leading digits)
1*(1+1)=2
2*100=200
200+50*(1-1)=200
200+25=225
15*15=225
Or:
15*35=525(the bigger leading digit always plus 1 not the smaller one)
1*(3+1)=4
4*100=400
400+50*(3-1)=500
500+25=525
15*35=525
The result is:((SLD)*(BLD+1))*100+50*(BLD-SLD)+25
SLD=Smaller leading digit
BLD=Bigger leading digit
So,if you accidentally add 1 to the smaller leading digit,the result is wrong!:
Example:35*15
3*(1+1)=6
6*100=600
600+50*(3-1)=700
700+25=725
But 35*15 is 525 not 725 so
That's why you should always add 1 to the bigger leading digit ONLY if the multiplication has the different leading digits from each number!
And as always,thanks for reading because it's cool!XD
Cool
The proof is amazingly brilliant!!!!
Last step: take the difference between 18 and 15 cents, which is 3 cents, and multiply by 14. This gives you 42 cents which you add to the 44.10 for 44.52.
Thank you very much.. :)
awesome trick
Easier math if you use $3.20/gal for the gas. And it even improves your estimate.
Yup !
But using this method is easier, that's why
i cant understand the average, how to solve that?
Very good trick
Cristobals method of Multiplying Endings of 5
15×35
1
3
1
=5 25 (even)
35×115
3
33
+4
40 25 (even)
the easier way without multiplying by 100 and avoiding decimals
15
x 35
-------
1 x 3 || 5 x 5
3 || 25
+ 2 0 -----> add the average of 10 + 30 (20) and put just before the unit's place
---------
= 525
65
x 75
-------
6 x 7 || 5 x 5
42 || 25
+ 6 5 ----> add the average of 60 + 70 (65) and put just before the unit's place
----------------
= 4875
An easier way to visualize this is to realize that if you were to divide a multiple of 5 by 10, it becomes adding a half.
For example = 42 * 15 = 10 * 42 * 1.5
In the above example, you are multiplying by 1 and a half. So, mentally you could take 42 + 21 = 63 and multiply by 10, to get 630.
However, this can be easily expanded by using any multiplication with multiples of 5. As simple as 54 * 5 = 270 (either by multiplying outright, or dividing by 2 and multiplying by 10).
This video takes the same principle, essentially. 45 * 45 for example is the same as 10 * 45 * 4.5 So, you multiply 45 by 4 (as stated above) to get 180, add half of 45 (22.5) 202.5 and multiply by 10, to get 2025.
Multiplication with 15 is also to think about when realizing, you can also divide by 2, and multiply by 3, and then by 10. 18 * 15 = 270 (divide 18 by 2, multiply by 3, and then multiply by 10).
There are lots of cool tricks out there. I just had noticed the commonality with the (adding the average) as essentially being the same as what I've been doing for years with thinking of the 5 as a half of 10, and then adding that on.
Where do you get all your ideas...?
Ancient Vedic Mathematics of India
Very very very much helpful
Also works in a very similar way if you have two numbers ending with 6... As long as you use base 12. :)
Just find a way of converting to base 12 from 10 easily.nu can convert from base 12 to 10 easily but u can't do it backwards easily
SlimThrull see my videos ..... I will be happy if I can help anyone
SlimThrull, how? Show us.
Very useful and explained nicely algebrically. Thanks.
We're did u get the average??
How Find theAverage ?
Welcome :)
Add those n numbers and divide by n
this was amazingly awesome trick sir
Thank you so much sir
You even gave an explanation to the sort trick. I like that part most
How did you come with the average numbers?
Each no multiply then divide by 2
nice trick's
It's nice... but how can you get the average very fast?
Actually i found it myself and came to check if it's already known
And as always someone has already done it 😂
I thought that's same as my method but now after watching video it's a bit different
I ll tell u my method
Add non last digits (numbers ending with 5 only, lets call the numbers x and y frm here) and then if it odd the result ends with 75 else ends with 25.
And now for the remaining
Add take average of the x and y as in the video and ignore the decimal
And add it to the multiplication result of x and y
It's the exact same thing but my method just reduces the hassle of decimal and all just try a few times u ll feel better this way
excellent algebraic explanation. This method works for others numbers too..great one.
this is just a small trick of vedic math just read whole vedic math you wont even need calculator for bigger problems
Let's taks your example
65x75
When their difference is 10 then
Write 75 in the left
After that
Multiply lower tens digit with higher tens digit plus 1 u will gwt the answer
__75
6x8= 48
Why we take 500
I understood 14×3.15=44.10
5:06 how do we get 14×3.18=44.52
Just add 14x0.3, that iš equal to 0.42 and 44.1+0.42=44.52 :)
Didn't work with 625x5 ?
hats off
how do you find the average
Thayananthan A if you cant find averages I suggest skipping this video...
add the two numbers and divide by 2
what do you mean? ;)
The average is WAY above YOU, buddy.
I m very impressed by this video
its not really the "leading digit" , but "all digits apart from the 5". One and the same for two digit numbers yes, but not beyond that.
You are just great! Born great can make others achieve greatness..........! Thanks a lot.
so how much can you alter 15555 * 15155?
15555*15155=
product : 1555*1515 = 2,355,825
average : (1555+1515)/2 = 3070/2 = 1,535
you add both product and average and you get : 2,357,360
you multiply by 100 to get : 235,736,000
and then you add 25 to get : 235,736,025
+IamA Troller you have to use the trick for the 1555*1515
you can use the trick or a calculator xDD
woah! mind blown
Cool 😃😃
it is so nice.
Yeah!
this will help me with homework ALOT
very useful
example 42 why the average is 6.5?
(6+7)/2 = 6.5
How do i calculate the average any body please tell me
Average= (sum of all digits)÷ no.of terms
Example- average of 2,3,4,5 ?
= (2+3+4+5)÷4
Learn Vedic mathematics
Awesome, you prove with proof.
He didnt prove
It is already proven in Ancient vedic mathematics
I have shortest way for this.... Worlds shortest
Super sir
good 1.
This technique of shortcut calculation is derived from ancient vedic mathematics
Dont u dare to use ur name as copyright of this technique
👍
Why we dont use our calculator??
How to find out the AVERAGE?
Where it come 100 & 25?
Ayan Ali 10 x 10 = 100. 5 x 5 = 25.
wow
That's fucking longer than what I learned at school
I could also use a calculator
O know.....w.gooood
your "proof" makes no sense, you don't even explain why you did 50(x+y) you just did it thats confusing and then the last step of factoring out 100, where did the 50 go?! like explain don't just say nonsense without explanation
Is these type of tricks for number ends with 6?
If yess then tell me plz.
easy way to multiply😂😂😂
This is awesome; This Is Awesome!
I didn't understand how to get the average! 😱
Add 2 numbers together then divide its by 2. For example 1 x 3 = ???. To find the average of 1*3=(1+3)/2 = 2. Therefore, the average number is 2.
🎄Thanks a lot! Merry Christmas! 🎄
@@a-z5439 actually you add all the numbers and divide by the number of digits you added for ex: 5+4+3= 12 divided by 3=4 so 4 is the average of 5,4,3 ☺️
thanku
Open a telegram channel
Thank you
Vedic Maths has easy way than this.
awesome!
This only works for 55 multiplication problems
False. It works for all problems in which both numbers end with 5, an infinite amount of problems.
You can make it 2 steps:
Add the product to the average,
Put 25 on the end
learn vedic math better you know about India and your attitude is going slightly average
Aman Kaushik see my videos ..... I will be happy if I can help anyone
Apurva Kaushik this, this is why i hate indians because they are saying that vedic maths is better and attacking people.
But how do you work out what 4x3.18=??.??
55*75
how do u find average?
Where you say "multiply by 100" I have taught "Put it in the 100s place."
28
thank you :)
R
how to get the average!!??
add both the numbers and divide by 2...u will get it
114
It is wrong do it for 15 and 25
175
Its vedic mathematics. Stop stealing. 😬😬😬
Yes bro
or u can use a calculator
lalit
The method is so much more harder 20sec waste
Then u r waste
Super tp
Sir, please show your face....... The world is not seeing a genius
Osm
Op video
Hkfl
Easy maybe if you know how to get the average, how do you get average 6.5 from 42? This part is not explained
6+7/2= 13/2= 6.5
Shubhangi Chaturvedi thanks for trying to explain but I am now more confused, how would I even come to think of this calculator from the number 42?
@@djchill1765 practice makes a man perfect ... Now after watching dis video I m multiplying these numbers without pen n paper
@@djchill1765 65*75 .... 6*7 /5*5
42 + avg of 6n 7 = 48.5 *100 +25= 4875
Shubhangi Chaturvedi I’m even more confused to be honest but thanks for trying, my main point is the title starts by saying easy method and I find nothing easy about any of the methods above