Today I will publish my blog on the article of my younger son Master Abhishek Anil Satpute. Now he is studying in the 11th Grade of Science Stream. In 2008, when he was in 7th Grade (Standard), he found one interesting method: Mathematical Tables. My elder son Master Aaswad Anil Satpute also found out so many interesting things in Mathematics since his 4th Grade (Standard). (Now he is in the last semester of Computer Engineering)
This Article by Abhishek Anil Satpute is written in his own way. I thank him for allowing me to publish his article.
Easy method for creating mathematical tables
Abhishek Anil Satpute
7th Grade (2008)
While studying the mathematical tables, I found one interesting method for creating
the tables.
the tables.
A) New Definitions:
1) Small Friends: Two numbers having their addition as 5 are known as Small Friends
2) Normal Friends: Two numbers having their addition as 10 are
known as Normal Friends.
known as Normal Friends.
3) Big Friends: Two numbers having their addition as 15 are
known as Big Friends.
known as Big Friends.
B) Table of friends:
Small Friends | Normal Friends
|
Big Friends
| |
1
|
4
|
9
|
14 NA
|
2
|
3
|
8
|
13 NA
|
3
|
2
|
7
|
12 NA
|
4
|
1
|
6
|
11 NA
|
5
|
0
|
5
|
10 NA
|
6
|
-
|
4
|
9
|
7
|
-
|
3
|
8
|
8
|
-
|
2
|
7
|
9
|
-
|
1
|
6
|
c) Procedure for creating unit-placed digits:
1) Take the number of which the table is to create. (A)
2) Write the unit digit of the double of the unit placed digit of (A). (B)
3) Write the friend number of the unit digit of (B) as given below. (C)
Digit in the units
|
Type of friends to be used
|
1, 5 or 7
| Small Friends (05)
|
2, 4, 6 or 8
| Normal Friends (10)
|
3 or 9
| Big Friends (15)
|
4) Write the friend number of the unit digit of (A) as given below. (D)
Digit in the units
| Type of friends to be used
|
1, 3, or 5
| Small Friends (05)
|
2, 4, 6 or 8
| Normal Friends (10)
|
7 or 9
| Big Friends (15)
|
5) Write 5 if (A) is odd & 0 if (A) is even.
6) Write the normal friend number of the unit digit of (D).
7) Write the normal friend number of the unit digit of (C).
8) Write the normal friend number of the unit digit of (B).
9) Write the normal friend number of the unit digit of (A).
10) Write the 10th multiple of (A).
D) Procedure for creating ten’s/hundred's placed digits:
Now we will write the ten’s placed digits of the table. We will follow a few simple
Rules as given below.
1) If ten’s placed digit of (A) is “0”, then while writing the table for (A), for Increasing
the digit in unit place, increment the ten’s placed digit by “0” else by “1”
2) If ten’s placed digit of (A) is “1”, then while writing the table for (A), for Increasing
a digit in unit place, increment the ten’s placed digit by “1” else by “2”
3) If ten’s placed digit of (A) is “2”, then while writing the table for (A), for Increasing
a digit in unit place, increment the ten’s placed digit by “2” else by “3” and so on.
E) Examples:
1) Table of 06 (A) Unit place is 6, so for the 3rd step take Normal Friends, for the 4th step take Normal Friends, and the ten’s placed digit is 0, so increment either by 0 or by 1.
01
|
Take the number 06 (A)
|
06
|
02
|
Double is 12, so take 2 (B). 2<6 so 0+1=1, so write 12.
|
12
|
03
|
Normal-friend of 2 is 8 (C) so take 8. 8>2 so 1+0=1, so write 18
|
18
|
04
|
Normal-friend of 6 is 4 (D), so take 4. 4<8 so 1+1=2, so write 24
|
24
|
05
|
6 (A) is Even so take 0, 0<4 so 2+1=3 so write 30
|
30
|
06
|
Normal-friend of (D) 4 is 6, so take 6, 6>0 so 3+0=3, so write 36
|
36
|
07
|
Normal-friend of (C) 8 is 2, so take 2, 2<6 so 3+1=4, so write 42
|
42
|
08
|
Normal-friend of (B) 2 is 8, so take 8, 8>6 so 4+0=4, so write 48
|
48
|
09
|
Normal-friend of (A) 6 is 4, so take 4, 4<6 so 4+1=5, so write 54
|
54
|
10
|
Always take 0, 0 < 4, so 5+1=6, so write 60
|
60
|
2) Table of 27 (A): Unit's place is 7, so for the 3rd step take Small Friends, for
4th step takes Big Friends, and the ten’s placed digit is 2, so increment either
by 2 or by 3.
01
|
Take the number 27 (A)
|
27
|
02
|
Double is 14, so take 4 (B). 4<7 so 2+3=5, so write 54.
|
54
|
03
|
Small-friend of 4 is 1 (C) so take 1. 1<4 so 5+3=8, so write 81
|
81
|
04
|
Big friend of 7 is 8 (D), so take 8. 8>1 so 8+2=10, so write 108
|
108
|
05
|
7 (A) is Odd so take 5, 5<8 so 10+3=13 so write 135
|
135
|
06
|
Normal friend of 8 (D) is 2, so take 2, 2<5 so 13+3=16, so write 162
|
162
|
07
|
Normal friend of 1 (C) is 9, so take 9, 9>2 so 16+2=18, so write 189
|
189
|
08
|
Normal-friend of 4 (B) is 6, so take 6, 6<9 so 18+3=21, so write 216
|
216
|
09
|
Normal-friend of 7 (A) is 3, so take 3, 3<6 so 21+3=24, so write 243
|
243
|
10
|
Always take 0, 0<3, so 24+3=27, so write 270
|
270
|
Once again I thank Master Abhishek for his article.
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