I love how you post these mental math tricks!! I hope you'd do more of them in the future, in particular multiplying large numbers (i.e. 54 x 26) and maybe a trick on subtraction as well.
16 x 16 = 16 + 6 x 10 = 22 x 10 = 220 then add 6 x 6 = 36 to get 256. This approach also work for any different number multiplication with the same 10's digit numbers i.e. 27 x 22 = 27 + 2 x 20 = 29 x 20 = 580 then add 7 x 2 = 14 to get 594 Algebraic method: (a+b)(a+c) = aa + ac + ba + bc = a(a + b + c) + bc However Krista's method (which was explained very clearly) is very powerful & easy to use. It can also be used for multiplication of numbers with different 10's digit & unit numbers. Algebraic method (a+b)(a-b) = aa - ab + ba - bb = a² - b² ∴ a² = (a + b)(a -b) + b² where a is the number to be squared and b is the difference to the nearest 10's value. But when dealing with two digit multiplication a is the average of the two numbers and b is half the difference between them so here we use (a + b)(a - b) = a² - b². e.g. 43 x 27: a = (43 + 27)/2 = 35 and b = (43 - 27)/2 = 8 ∴ 43 x 27 = 35² - 8² = 1225 - 64 = 1161
Okay,what if we round the first number to a number which is less than the original one?do we add to the second number the difference or do we do what you did in the video with all cases?
If you round the first number down, then you go up with the second number. It's always opposite direction. So for example, 13*13, you'd take the first 13 down to 10, and therefore the second 13 up to 16. 16*10=160, then add 3^2=9 to get 169. :)
Thank you so much! I have one short video on laws of logs (I'm hoping to make more!), and then I have several videos on derivatives with logarithms and integrals with logarithms. :) ru-vid.comsearch?query=logarithm
It's just different than purely taking the number and multiplying it by itself. Trying to multiply a large number by itself can start to become challenging, so this is just a different way to approach that problem. :)
Huh? 'Multiplication of squares.' That's the title. You can't use 13 x 13 as an example in a video called 'multiplication of squares' because THIRTEEN ISN'T A SQUARE! Thirteen is prime, for crying out loud. I can't believe I'm having to explain this.
"A different way to multiply squares!" is the title. When you are evaluating 13^2, you are multiplying out a square. Literally. Look at a square with a side length 13 units. Does the area not exist based on your logic? You're multiplying out a square when you evaluate any real number raised to the power of 2.
Huh? Consider the phrase 'multiplying primes.' You'll agree that to multiply primes, you have to start with primes, yes? Consider the phrase 'multiplying odd numbers.' You'll agree that to multiply odd numbers, you have to start with odd numbers, yes? Consider the phrase 'mltiplying squares.' To do that, you have to start with squarea, and 13 is not a square. You know what a square is, right? A square is a number with an integral square root, like 16 or 64 or 144. Those are squares. A problem like 16 x 144 would be an example of ' multiplying squares.' Thirteen x thirteen is not and cannot be an example of ' multiplying squares.' What say you, Krista?
Yes, but primes, odd numbers, and even numbers do not have multiplications embedded within their definition. A square _can_ be defined as something raised to the second power. When you multiply a square using *that* context, you are evaluating an expression like 13 x 13, 13^2. 13^2 is a square. The video is *obviously* using *that* context.
