20210426, 12:17  #1 
"Tucker Kao"
Jan 2020
Head Base M168202123
2^{2}·107 Posts 
What's the Name of This Calculation Method?
At first, I thought this was the Common Core Additions and Subtractions. I asked several neighbors and they said this was a totally different thing.
I'm wondering whether there's a given name for the specific calculation method showing on the screenshot below or is it my own way to count? 
20210426, 13:09  #2 
Apr 2010
Over the rainbow
5100_{8} Posts 
decimal base, octal base and a dozenal base? i don't know.

20210426, 13:39  #3 
Feb 2017
Nowhere
3·1,601 Posts 
This is simply regrouping and reassociating. I admit I don't see much point in doing things this way. One could equally well say 6 + 7 + 5 = 6 + 2 + 5 + 5 = 8 + 10 rather than 6 + 4 + 3 + 5 = 10 + 8.
There are wellknown methods of doing the equivalent in addition and subtraction. With addition, it is called "carrying," and with subtraction, it is called "borrowing." EXERCISE: Let m and n be positive integers in base b (b > 1 integer). The sum of the baseb digits of m + n is equal to the sum of the baseb digits of m and the baseb digits of n, minus (b1) times the number of carries in the baseb addition of m + n. Last fiddled with by Dr Sardonicus on 20210426 at 13:39 
20210426, 14:01  #4 
"Tucker Kao"
Jan 2020
Head Base M168202123
2^{2}·107 Posts 
Common Core Math does try to get rid of the carrying and the borrowing, instead using the distance between the numbers to figure out the sum or the difference.
I admit the method is slower when calculating only in the decimal base, but when I calculate them in other bases with the larger numbers like the screenshot showing below, I no longer need the base conversion calculators, also no hard additions or subtractions from the alternative bases. When applying the carrying and the borrowing in other bases, it requires the person to memorize the entire addition, subtraction, maybe multiplication tables of other bases to avoid making frequent mistakes on the larger numbers. With the method I use, a person only needs to memorize: [Octal] 1 + 7 = 10 2 + 6 = 10 3 + 5 = 10 4 + 4 = 10 10  1 = 7 10  2 = 6 10  3 = 5 10  4 = 4 [/Octal] [Dozenal] 1 + Ɛ = 10 2 + Ӿ = 10 3 + 9 = 10 4 + 8 = 10 5 + 7 = 10 6 + 6 = 10 10  1 = Ɛ 10  2 = Ӿ 10  3 = 9 10  4 = 8 10  5 = 7 10  6 = 6 [/Dozenal] The total amount of the unique formula needs to be memorized equals to the base itself, so pretty much only involves those formula of the 10 of the given base or with the sum under its 10 of that base. Last fiddled with by tuckerkao on 20210426 at 14:41 
20210426, 15:44  #5  
Feb 2017
Nowhere
11303_{8} Posts 
Quote:
Coupled with the alleged difficulty of memorizing arithmetic tables for the digits of other bases (which IMO you pretty much have to do anyway to use the regrouping and reassociating you describe), this makes an excellent argument for avoiding more than a cursory introduction to actually doing arithmetic by hand in bases other than decimal. Better to get a decent command of doing decimal arithmetic, and then realize that the same basic principles and methods apply to any base. You might enjoy this Tom Lehrer song about the "New Math" 

20210426, 15:50  #6 
Jan 2021
California
178_{10} Posts 
Well, if the US had ever gone metric...

20210426, 16:10  #7 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
6,257 Posts 
... anything.
Addition and subtraction aren't hard. They aren't difficult. They aren't actually a problem at all. They are easy. The problem seems to be the perception a lot of people have. "Eww, adding? That's maths, and therefore it's too hard. What's the latest nonsense on Facebook that I can get angry about?" 
20210426, 16:13  #8 
Feb 2017
Nowhere
3×1,601 Posts 
Even though I grew up with teaspoons, tablespoons, ounces, cups, pints, gallons, inches, feet, yards, and miles, I did all the arithmetic in decimal.
When introduced to metric units, I was immediately impressed by the fact that a cc of water was very nearly a gram, and a liter was 1000 cc's. I liked to ask, "Quick  how many cubic inches in a pint?" I later learned that the US standard for liquid measure was the US gallon, which by definition is 231 cubic inches. So, a pint is 28 and 7/8 cubic inches. I am duly grateful that the good ol' USA had a decimal money system long before the UK 
20210426, 16:38  #9 
Apr 2010
Over the rainbow
2624_{10} Posts 
Multiplication and division , in other base than 10 isn't very intuitive
Last fiddled with by firejuggler on 20210426 at 16:57 
20210426, 17:40  #10 
Jan 2021
California
2×89 Posts 

20210426, 23:36  #11  
"Tucker Kao"
Jan 2020
Head Base M168202123
654_{8} Posts 
Quote:
9 + ? = 10 [Dozenal]9 + 3 = 10 [Hex]9 + 7 = 10 For Bases smaller than Decimal  10  1 = ? [Octal]10  1 = 7 [Senary]10  1 = 5 [Binary]10  1 = 1 Using the alternative methods have the strength to avoid the instant to operate decimal base when calculating in other bases, thus people will try to figure out the distance between each number first. Like Feb 29 in the leap year, the additional numerical become the leap numbers, so 02/28/1996 + 2 days = 03/01/1996 Quote:
[Dozenal] ӾƐ + 7Ӿ = ӾƐ + 11 + 69 = 100 + 69 = 169 [Dozenal] Ӿ7 + ƐӾ = Ӿ7 + 15 + Ӿ5 = 100 + Ӿ5 = 1Ӿ5 or [Dozenal] Ӿ7 + ƐӾ = Ӿ7 + 100  2 = 1Ӿ7  2 = 1Ӿ5 [Hex] 8 + 9 = 9 + 8 = 9 + 7 + 1 = 10 + 1 = 11, thus it has been calculated independently from the decimal base. [Hex] 11  8 = ? ...... 8 + 1 = 9; 9 + 7 = 10, 10 + 1 = 11 ...... 1 + 7 + 1 = 9 Last fiddled with by tuckerkao on 20210427 at 00:34 

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