How to multiply any 2-digit number by a 2-digit number
HTML-код
- Опубликовано: 2 июн 2024
- A quick tutorial on multiplying any two-digit number by another two-digit number. I think this is faster and better, especially for bigger numbers. I will provide 3 examples and explaination of the method. Let me know what do you think about this method.
Shop my math t-shirts & hoodies on Amazon: 👉 amzn.to/3qBeuw6
-----------------------------
I help students master the basics of math. You can show your support and help me create even better content by becoming a patron on Patreon 👉 / blackpenredpen . Every bit of support means the world to me and motivates me to keep bringing you the best math lessons! Thank you!
-----------------------------
#math #algebra #mathbasics
0:00 3 examples
2:07 Explanation for 25 x 41
3:48 Explanation for 74 x 68
From Reddit: 9*(-8)*7÷(-5) = ?
Answer here: ruclips.net/video/toKCCap53wo/видео.html
Welcome back to another episode of "Why wasn't I taught this in elementary?"
Because it is irrelevant.
Might not have been elementary but it was during algebra. This is just the foil method without the variables essentially.
@@tigerlover7359 exactly. This is not a good video.
Well its just another way..ur doing exatly the same...
..and it should also work for long digit number, but it will be alot mor work and not so intuitive...as u have to move to 10ths, 100ds, 1000 and so on
..in wich way the standard works just fine for unlimited digits... (no cluttering digits everywhere)
@@Patrik6920 yeah.
1:08 you make a small error by saying 2×8=10
was gonna point it out too
@euloge996 You just made an error pointing that he made an error but in reality he didn't He just made an error while speaking it's 2 + 8 not 2 times 8 but that's neglected as he's calculus master and arithmetic errors are a part of almighty master's life
@@ArjunDzn I know he made a speaking error not a mathematical error, my comment literally says "a small error by SAYING". I know that he is very good mathematician I just wanted to point it out so that people wouldn't get confused or anythingm
@@euloge996 haha gotchu btw my reply was just a sarcasm
I'm late by 8 hours... 🙂
We weren't taught this as it doesn't simplify the calculation, only it can be done in one line. It takes the same amount of time as the traditional way.
Similar to the FOIL method used for binomials, but a different application.
Also, not really "better" than the standard method.
It is better when you apply it on mental calculation. The reason why traditional method is hard to do mentally is because there's so much to remember
Do some more vids on this super basic stuff I feel it is somthing most math students including myself neglect
This will truly help me during studies. Thanks sir!
Similarly, we can multiply any 3-digit number by any 3-digit number: for abc × def, we consider (ax² + bx + c)(dx² + ex + f) = adx⁴ + (ae + bd)x³ + (af + be + cd)x² + (bf + ce)x + cf, where x = 10. Then, we have abc × def = {ad}{ae + bd}{af + be + cd}{bf + ce}{cf}, where {・} represents a digit.
Sure ... very "useful".
I assume x here represents 10, since we count in base 10. You are absolutely right, but this would be very hard for students, if they had to memorize a different multiplication method for every possible combination of factor lengths.
Is this supposed to be helpful?
amazing! I'd love to learn even more fast motheds like this one from you ❤
Now i have a challange for you sir
( Actually i need help with this question)
Find the value of x and y without making a 4 degree equation for the following
x + y +xy =11 and
x^2y + xy^2 =30
This question is a brain teaser given by my teacher we we couldn't figure out becuase we are just 15/16yrs old Lads
This isn't revolutionary. This is the completely standard multiplication algorithm we all learned in school, except you just typeset it a little differently. Maybe saving a little space, but apart from that there is literally not a single reason to use it over the standard algorithm.
But the standard way to write down this multiplication algorithm generalizes almost trivially to larger numbers, while this method becomes unwieldy almost immediately, so that's a very good reason to just keep using that.
What is very nice about the last one is that 74 is extremely close to 75, and 4 divides 68. So we multiply by 3/4 and by 100. From there we subtract 68 once
Are you a pro in maths
The application of the FOIL method.
Yup
Just Calculate: (10 x 22) + (3 x 22).
I attented in mental multiplication competitions like Memoriad, but I think it‘s still the easiest way for untrained persons to multiply smaller digit numbers.
If there is an even difference between the factors, for example: 25 x 35
Difference: 35 -25 = 10
Then you can calculate (30 x 30 ) - 5^2. So: 900 - 25 = 875.
I know all squares from 1-99 from memory, so I can use it more often.
If a number is near a full tenth, for example 48 in: 48 x 36
Then calculate (50 x 36) - (2 x 36) = 1728.
this is one of my favourite methods for 2 or 3 digit products, i use it a lot for beginner math competitions.
This is how I personally format this method, along with how to involve 3 digits (or more, if you extend the pattern), the slashes are just partitions to keep it clear:
3 digit times 2 digit
abc
x de
--------------------------------
ad/ae+bd/be+cd/ce
--------------------------------
(answer)
3 digit times 3 digit
abc
x def
-----------------------------------------------
ad/ae+bd/af+be+cd/bf+ce/cf
---------‐-------------------------------------
(answer)
u r a supersmart.
This is just the FOIL method in disguise.
Yes
@@bprpmathbasics but with less writing, since we can remember the intermediate results
is there a way to do with 3 digits?
I prefer just going right to left. I did UIL Number Sense competitions for three years in school and you had to do all the math in your head and only write down the answer or you missed it. It's not that hard to remember the carries as you go, at least for me.
I still love to mess with numbers just to distribute them and solve big products or big divisions
1:07 - dont you mean 2 plus 8 ?
Yes
1:10 u mean 2 + 8 right
Yes
Criss Cross Apple Sauce!!!
FOIL?
This is literally the same as doing it normally wich is very slow compared simplifying it in any other way, like the right and left parts are literally the same in my mind, if i use your method i can't unsee in my mind the normal way ( left side) wich is something i would never use.
Isnt this foil method master?
Why dont we learn this in school 💀
Definitely not easier no.
The stack method where you multiply each digit of one number with the other number, put the result in a row, and add the rows, is the same ammount of work. The difference is everything is more explicitly written out, and each result is given a dedicated place to be written, making the addition part easier. Because you have less structure to where things are written down when using your method, it is technically faster, but at the cost of being much less tidy and more prone to errors. Additionally, the stack method is great for dealing with large numbers, since a larger number only leads to additional rows being added to the stack. With your foil method, it is not as obvious how to do the multiplication for larger numbers.
I would say your method is good for experienced mathematicians, whenever you don't have a calculator and need to quickly solve a multiplication, but the stack method is much more versatile and likely easier to teach.
For 74×68, all you have to do is use the difference of squares. 71x71 is 5041, and each number is plus or minus 3 away from 71, so you subtract 3x3, or 9. Answer: 5032. It took me about one second to calculate.
OR, just do the FOIL method instead of squares. You're just making the equation longer for yourself
1:11 u said multiplication instead of addition lmao
It's like FOIL o.o
Why wasnt i taught this
It only works for two two-digit numbers and isn't any faster.
yes , a calculator
Hard pass. Really this isn't doing anything different than the standard method. Horizontally versus vertically written, I guess. Silliness.
You can't hard pass a method. It exists, you can't just pass it
In what way is this "better"? Changing the ORDER of which digits you multiply changes NOTHING!
Hi! i think this trick takes almost the same time than the traditional... And you appeal to the old way to understand the fast way... ironic, doesn't it? Greetings from Montevideo (Uruguay)
this method is not faster than traditional multiplication. meh.
... there is nothing new about this.
... which implies nothing better.
Point out where anyone claimed it was new
@@ZackBlackwood97 why? Point out where I claimed someone claimed it was new. That's not the point.
This is just bad. For more than one reason. First, let's take each example:
1) 13×22
Multiplying by multiples of 11, let's say 11n, multiply by n then multiply by 11. In this case,
13×22 = 26×11 = 286
immediately. Let's compare this with a big multiple,
73×88
My method:
73×88 = 584×11 = 6424
immediately.
By the method in the video:
73×88 = 56..56+24..24
= 56..80+2..4
= 56+8..2..4
= 6424
which may be easy to see, but I bet many people would not be able to make this calculation, making confusions in some steps.
2) 25×41
Man, really? Just do
25×(40+1) = 25×40+25×1
= 1000+25
= 1025
Done. I am not even compare this one.
3) 74×68
Use 5,
74×68 = 75×68-68
= 150×34-68
= 300×17-68
= 5100-68
= 5032
or complete 68 to get 70,
74×68 = 74×70-74×2
= 5180-148
= 5032.
These are great tricks and there's always a way to find one, with easier factor and a substraction. The video was about doing the multiplication the stack/foil way without writing it, thanks to the fact it's easy to memorize the temp results. Works everytime without the need to find an optimization
@@cheeseparis1 I don't know man. Certainly the order he make the calculations is not effective. I mean, better follow the sequence of steps
74×68
= ..32
= (56+24+3)..2
= 83..2
= (42+8)..32
= 5032
So, if we are talking about mental calculation, this is the way. If we are talling about calculation on paper, I think it makes no sense to write or teach such calculation.
@samueldeandrade8535 you're just making equations unnecessarily longer for no reason though. You wrote whole ass paragraphs for 13×22.
@@ZackBlackwood97 you don't get the point. And I will not waste my time explaining to someone who clearly doesn't want a normal conversation. Have a nice day, boy.