37-Easy Method For Creating Mathematical Table

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.

  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.

  3) Big Friends: Two numbers having their addition as 15 are 
      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 place	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 place	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.

Anil Satpute

36-Simple Method of Multiplication

Today we will see the simple method of Multiplication. We are all aware that while doing multiplication, we need to take a product of say higher digit 9 with another 9 that comes out as 81. then we write 1 and keep carry as 8 and the same business we do till we get the answer. Here I simply do the same thing but no carry business is kept to remember.

Actually, this is a very simple method and without any error and within a very short period, we can do the multiplication.

Please see the following example of multiplication

Example: Multiply  279 by 563.

Step-01:
1) Here 279 is Multiplicand and 563 is a multiplier.
2) Unit's digit of Multiplicand 279 is 9.
3) Unit's digit of Multiplier 563 is 3.
4) The product of 9 and 3 is 27, which is written as it is as shown below.

5) Here the Number 27 obtained by the product of 9 & 3 has the unit's digit as 7 & the ten's digit as 2 and the same is written as it is, as shown below.
6) The ten's digit of Multiplicand 279 is 7 and that of Multiplier 563 is 6 and the product of 7 & 6 comes out as 42, which is written at Hundreds and thousands of places as shown in the diagram.
7) In the same way, the product of Hundreds of digits of Multiplicand & Multiplier is 2 into 5 is 10 which is also written as it is.
8) the corresponding product of the digits is written and below the digits 1 and 7, we put the Star mark so that those places are not used to write the product of the digit in the 2nd step.


Step-02:
1) The product of Ten's digit of Multiplicand (279) say "7" and the unit's digit of Multiplier (563) say "3" is 21 and the same one is written as shown below.
2) In the same way, the Product of the Hundreds digit of  Multiplicand (279) say  "2" and the tens digit of Multiplier (563) say "6" is 12 & is written as shown in the adjoining diagram.










Step-03:
1) Similarly, the product of the Unit's digit of 279  say "9" & ten's digit of 563 say "6" is 54 is written as shown below.

2) The product of ten's digit 7 of 279 & hundreds digit 5 of 563 is 35 is written as shown in the adjoining figure.
3) Now block the places below 3 & 4 of the number 3554 & allow to write below 55 as shown in the adjoining diagram.












Step-04:
1) Now the product of Units of 279 say "9" &  Hundreds of 563 say "5" is 45 & the product of Hundreds of

279 say "2" & Units 563 say "3" which is "06" (Note: Always we need to take two digits of the product of any two digits. We know that the single largest digit is 9 & the product of 9 & 9 is 81 which is two digits, so any product of single two digits should be written as two digits number only.). So here we need to write 45 & 06 one below the other as shown in the adjoining diagram.
2) Then simply take the vertical addition. This is your final answer.










Like this, you can take the product of a 4-digit number & 3-digit number. Only we need to put "0" at the ten-thousands place to make our Multiplier of 4- digit Numbers.

Please study the above method & try it by doing some more product with the help of your parents. You can also ask me your query if any by filling out the Entry form available at the top left tab of this blog.

Enjoy Learning Mathematics by creating such type of interesting things.

Anil Satpute

35-Basics of Trigonometry - 21 Important key points

Click here for the previous basics of trigonometry.

See the simple method of calculations for solving the Trigonometry Problem. There are so many methods to solve such types of problems. You also may have a better solution for such types of problems, that can also share with other students. Please see the following problem & its solution which I find an easier one. If you have any other simple method, then please publish your method through this blog simply by writing comments.

Observe the above problem & its solution. So many books have different types of solutions. Basically, the problem will be very simple if you convert them into Sine (sin) & Cosine (cos) ratios (functions). Calculations will become very easy.

Remember well that the above method is authentic.  All the mathematical, simple formulae (formulas) are used.

I simply don't want to tell you to go with this simple method of calculation. I want that slowly, you need to mold yourself and improve your thinking level. Only using this technique for solving some problems and getting good scores will not serve my purpose. I want the entire world to improve its thinking skills so that everyone can invent so many beautiful things in human life.

This is possible only with the help of students like you along with your parents.

Please come ahead and start this beautiful work for yourself and show the world that we can also build the world with powerful thinking levels as everyone is competent.

ANIL SATPUTE

34-Problem on Circle 1

It is a problem for Students of 10^th Standard / 10^th grade. I would like to share the method of solving the problem & its presentation with you. Please go through it & make the habit of applying the same technique to solve other problems & please share this technique with your friends & relatives. (Please note one thing “By distributing our knowledge, it will boost & by keeping it only with us, it will reduce”).

   

Please see the following Problem.

I found some easier methods for this problem. so I would like to share this method with you. I am sure, that you may also find some easier methods than this. so Please come forward to share your method also.

Two non-congruent circles touch each other externally. The sum of their areas is 298 π square centimeters and the distance between their centers is 20 cm. Find the radii of both circles.

Solution

1)    Let the radii of the circles be r₁ & r₂

2)    As the circles touch each other externally,  r₁ + r₂ = 20 cm

 So    r₂ = 20 - r₁

3)   Sum of areas of circles  = 298 π

So               π r₁² + π r₂² = 298 π

                           r₁² + r₂² = 298

            r₁² + r₂² + 2 r₁ r₂ - 2 r₁ r₂ = 298

                           (r₁ + r₂)²- 2 r₁ r₂ = 298     put (r₁ + r₂) = 20

                                (20)²- 2 r₁ r₂ = 298 

                                   (20)²- 298 = 2 r₁ r₂

 400- 298 = 2 r₁ r₂         Dividing Numerator &

                                        Denominator by 2

 200- 149 = r₁ r₂

            51 = r₁ r₂

          r₁ r₂ = 51            put the r₂ = (20 - r₁)

            r₁ (20 - r₁) = 51

             20 r₁ - r₁² = 51

     r₁² - 20 r₁ + 51 = 0

r₁² - 17 r₁ - 3 r₁ + 51 = 0

    r₁ (r₁ – 17) – 3 (r₁ – 17) = 0

     (r₁ – 17) (r₁ – 3) = 0

    So r₁ = 17 or   r₁ = 3

4)    So the radii of the circles are 17 cm & 3 cm.

Like this, you can apply the technique to make use of simple calculations.

I hope, you will definitely implement this technique to save you valuable time on Examinations or tests. The same logical thinking can be applied to improve your thinking level.

I simply don't want to tell you to go with this simple method of calculation. I want that slowly, you need to mold yourself and improve your thinking level. Only using this technique for solving some problems and getting good scores will not serve my purpose. I want that the entire world needs to improve its thinking skills so that everyone can invent so many beautiful things in human life.

This is possible only with the help of students like you along with your parents.

Please come ahead and start this beautiful work for yourself and show the world that we can also build the world with powerful thinking levels as everyone is competent.

Anil Satpute

33-Basics of Trigonometry - 20 Important key points

Click here for the previous basics of trigonometry.

It is a problem for Students of 10^th Standard / 10^th grade. I would like to share the method of solving the problem & its presentation with you. Please go through it & make the habit of applying the same technique to solve other problems & please share this technique with your friends & relatives. (Please note one thing “By distributing our knowledge, it will boost & by keeping it only with us, it will reduce”).

   

Please see the following Problem.

So many books solved this problem with so many different methods. I found some easier methods for this problem. so I would like to share this method with you. I am sure, that you may also find some easier methods than this. so Please come forward to share your method also.

Like this, you can apply the technique to make use of simple calculations.

I hope, you will definitely implement this technique to save you valuable time for Examinations or tests. The same logical thinking can be applied to improve your thinking level.

I simply don't want to tell you to go with this simple method of calculation. I want that slowly, you need to mold yourself and improve your thinking level. Only using this technique for solving some problems and getting good scores will not serve my purpose. I want that the entire world needs to improve its thinking skills so that everyone can invent so many beautiful things in human life.

This is possible only with the help of students like you along with your parents.

Please come ahead and start this beautiful work for yourself and show the world that we can also build the world with powerful thinking levels as everyone is competent.

Click here for the next basics of trigonometry.

ANIL SATPUTE

32-Basics of Trigonometry - 19 Important key points

Click here for the previous basics of trigonometry.

It is a problem for Students of 10^th Standard / 10^th grade. I would like to share the method of solving the problem & its presentation with you. Please go through it & make the habit of applying the same technique to solve other problems & please share this technique with your friends & relatives. (Please note one thing “By distributing our knowledge, it will boost & by keeping it only with us, it will reduce”).

   

Please see the following Problem.

So many books solved this problem with so many different methods. I found some easier methods for this problem. so I would like to share this method with you. I am sure, that you may also find some easier methods than this. so Please come forward to share your method also.

Like this, you can apply the technique to make use of simple calculations.

I hope you will definitely implement this technique to save you valuable time for Examinations or tests. The same logical thinking can be applied to improve your thinking level.

I simply don't want to tell you to go with this simple method of calculation. I want that slowly, you need to mold yourself and improve your thinking level. Only using this technique for solving some problems and getting good scores will not serve my purpose. I want that the entire world needs to improve its thinking skills so that everyone can invent so many beautiful things in human life.

This is possible only with the help of students like you along with your parents.

Please come ahead and start this beautiful work for yourself and show the world that we can also build the world with powerful thinking levels as everyone is competent.

Click here for the next basics of trigonometry.

ANIL SATPUTE

31-Basics of Trigonometry - 18 Important key points

Click here for the previous basics of trigonometry.

It is a problem for Students of 10^th Standard / 10^th grade. I would like to share the method of solving the problem & its presentation with you. Please go through it & make the habit of applying the same technique to solve other problems & please share this technique with your friends & relatives. (Please note one thing “By distributing our knowledge, it will boost & by keeping it only with us, it will reduce”).

   

Please see the following Problem.

So many books solved this problem with so many different methods. I found some easier methods for this problem. so I would like to share this method with you. I am sure, that you may also find some easier methods than this. so Please come forward to share your method also.

Like this, you can apply the technique to make use of simple calculations.

I hope, you will definitely implement this technique to save you valuable time for Examinations or tests. The same logical thinking can be applied to improve your thinking level.

I simply don't want to tell you to go with this simple method of calculation. I want that slowly, you need to mold yourself and improve your thinking level. Only using this technique for solving some problems and getting good scores will not serve my purpose. I want that the entire world needs to improve its thinking skills so that everyone can invent so many beautiful things in human life.

This is possible only with the help of students like you along with your parents.

Please come ahead and start this beautiful work for yourself and show the world that we can also build the world with powerful thinking levels as everyone is competent.

Click here for the next basics of trigonometry.

ANIL SATPUTE