French Finger Calculator and Counting With Fingers
Motive and Evidence
I had a hard time using Purpose multiplication tables when I was a child. I was very confused. My teacher said that I should use my hands for my hands for multiplication tables . I was very surprised,but I didn’t think that it was mysterious when I was a child. However, I think that it is Result:
mysterious now. Therefore, I thought. II’d like to prove the French Finger d like to prove the French Finger Calculator and Counting With Fingers. I want to look at the case of multiplying two digits × two digits. thousand tens
1924 Yuki Tanaka
First I want to prove Counting With Fingers. The left hand’s number is x. The right hand’s number is y.
So the number of standing finger is :
Right hand (10‐x)
Right hand (10
x)
Left hand (10‐y)
The number of bent finger is :
Right hand (x‐5) Left hand (y‐5)
The number of tens is (x‐5)+(y‐5)
And the number of digits is (10‐x)(10‐y)
10{(x‐5)+(y‐5)}+(10‐x)(10‐y)=xy
10(x‐y‐10)+100‐10x‐10y+xy=xy
10x‐10y‐100+100‐10x‐10y+xy=xy
It was proven.
Method
Counting With Fingers
For example,I’ll take 7×9
①For example,I’ll take 7÷5
7÷5=1… 2
So I will bend 2 fingers.
②For example,I’ll take 9÷5
9÷5=1…
hundred
digits
So I will bend 4 fingers.
The total number of bent fingers will be equal to the number of tens (6)
be equal to the number of tens.(6)
The number of digits will be the multiplication of the standing.(3)
7×9=60+3=63
French Finger Calculator
For example,I’ll take 7×9
① 7 is shown by the left hand.
From the thumb sequentially.
② 9 is shown on the right hand in the h
h
h h d
h
same way.
The number of tens is the sum of standing fingers.
The number of digits is the multiplication of standing fingers.
7×9=60+3=63
In the case of (11×15),(12×14)and(13×13)
In the case of (11×15)
(12×14)and(13×13)
You must use a special rule.
Using the counting fingers method, the answer is: 100+10(total number of
bent fingers)+(multiplication of bent
fingers)
Using the French Finger Calculator the answer:(ordinary result)+120
Result:
Next I want to prove French Finger Calculator.
The Right hand’s number is x.
The left hand’s number is y.
So the number of standing finger is :
Right hand (x‐5)
Left hand (y‐5)
The number of bent finger is :
Right hand’s (10‐x)
Left hand’s (10‐y)
Left hand
s (10 y)
10{(x‐5)+(y‐5)}+(10‐x)(10‐y)=xy
Result:
10(x+y‐10)+100‐10x‐10y+xy=xy
10x‐10y‐100+100‐10x‐10y+xy=xy
It was proven.
Next I want to prove Counting With Fingers.
(this time two digits × two digits）
Right hand’s number is x.
Left hand’s number is y.
y
So the number of standing finger is :
Right hand’s (x‐10)
Left hand’s (y‐10)
The number of tens is (x‐10)(y‐10)
The number of digits is (x‐10)(y‐10)
And 10{(x‐10)+(x‐10)}+(x‐10)(y‐10)
10(x+y‐20)+(xy‐10x‐10y+100)+100=xy
10x+10y‐200+xy‐10x‐10y+100+100=xy
It was proven.
１２×１４、１３×１３、１１×１５ calculates by French Finger Calculator. Opposite is an example of this rule.(see example here ↓)
Standing finger+Standing finger=4 Bent finger+Bent finger=6 Right hand is x . Left hand is y.120 is n.
12
14
The number of standing finger is :
Right hand (15‐x)
3
1
Left hand (15‐y)
The number of bent finger is :
Reference Right hand (x‐10)
2
4
literature
Left hand (y‐10)
Suugakutamatebako
Therefore,
http://izumi‐
（１５ ）＋（１５ ） ４
（１５−x）＋（１５−y）＝４、
math.jp/sanae/Math
11
Topics/MathTopics.
30‐x‐y=4,‐x‐y=26…①
htm
(x‐10)+(y‐10)=6,x+y‐20=6
4
x+y=26…②
xy=10{(15‐x)+(15+y)}+(x‐10)‐(y‐10)+n
1
xy=10(30‐x‐y)+(xy‐10x‐10y+100)+n
Result:
xy=300‐10x‐10y+xy‐10x‐10y+100+n
Put on the answer from ①
‐260+xy‐260+100+n]
xy‐xy‐n=300‐260‐260+100
‐n=‐120 n=120
It was proven.
13
2
3
15
0
5