Simplification Tricks By Vikas Ghode Part 1

Hello, Friends...

Today we are going to learn some simple but very effective techniques for solving Simplification examples. As always these tricks are not always effective on every example as bank exam paper setters are very good than we think.

Simple addition & Multiplication techniques :

as we know addition & multiplications is basic to all maths, we are covering this topic for mind calculations only. Meaning you don't need to use pen & paper for solving this type of questions. 

first upon we need tables at least up to  29 besides squares & cubes.

But I tell you first, forget all the tables that you remember. Since there are very effective & 100% working techniques for doing these 3 things. & as you do it in ur mind, u will be sure of results.

Do you know how much 29X7 = ? 

If you are so sure with recited tables then its good but if you don't know then this is just piece of cake.

Here it is 

29 X 7 = (20+9) X 7

= 140 + 63 
....(This is most Simple for mind calc. Forget all other tricks)

Now just add Tens places, 

 Since unit's places are always 0 & (Unit place of 7 X 9) i.e. 0 + 3 & you don’t need to add this since they are obvious. 

Now tens places are 14 & 6, So 20, answer is 203

Now take exercise & Answers are provided nowhere...

1. 130 X 7
2. 42 x 5
3. 71 X 6
4. 23 X 6
5. 44 X 9
6. 55 X 0.75
7. 3 X 97
8. 19 X 7
9. 17 X 8
10. 16 X 6

Hey I have more tricks too,

Trick 1 : Let me tell you one thing, as there is no tricks in maths, I cant say any technique as trick. Remember, C-Language is Language of Computer, while Math is language of Gods...

All tricks are just applications of maths, as we can eat by more than one way, same way we can calculate with more than one way.

Please say once the table of 13, 17, 19, 23 & 29.

Why because I know if you have recited them in 10th then you will know at least up to 5 meaning 13 ones are 13, 13 twos are 26 till 13 fives are 65...ok we want just up to 5

Now what about 13 six are?

Simple

 13 x 6 = (13 x 3) x 2 = 39 X 2 = 40 x 2 - 2 = 78

Is that cool? just half the other & double after multiplication

Another example 13 x 8 = 

1. First 13 x 4 => 52 X 2 => 50 + 50 + 2 + 2  = 104

Now 13 x 9 = 130 - 13

= (13 X 4)X 2 + 13 = 104 + 13 = 1-1-7 = 117

Pretty simple, lets try bit difficult...

29 x 6 = ? 

Table is as follows

29, 58, 87, 116, 145

Now 29 x 3 => 87 X 2 => 174

OR 29 x 6 = (30-1)x 6 = 180 - 6 = 174

Again, 29 x 9 = (30-1) x 9 = 270 - 9 = 261

OR 29 x 9 = (29 x 4)x 2 + 29 = 116 x 2+29 = 232 + 29 = 261

Sorry for UN-structured writing...I have blogging that's why. But as being professor I have to do.

One Last Trick :
Whenever you try to create table of 11-19 there is a trick for creating such tables. It is just 1 step removed from traditional multiplication. Lets see what it is...
Say, you want to multiply 13X7
then what we generally do is,

                    1 3
                    X 7
                    --------   
                    Ans here

Then

                     2<--Carry

                    1 3

                    X 7

                    --------   

                        1 

Then

                          2<--Carry
                          1 3
                          x 7
                    -------------   
                    (7+2)1

Here , Instead of multiplying 1x7, we just add 2 & 7. Its because after the multiplication we obviously going to get 7. That's why we avoid multiplying & directly adding carry to multiplicand. See another example,

 12x8 = 6 & 1+8 = 96
17x9 =  3 & 9+6 = 153
14x8 =  2 & 3+8 = 112 (14x4   x2 = 56+56 = 112) 

Don't pay special attention to order in which I'm doing all these tricks, after all, these are mind tricks & you can do as per your convenience.

 
Trick 2: For Adding

Hey I'm not going to tell you how add numbers, I know a simple addition( Calculation) exercise that 100% develop your brain for adding anything, yes anything you can add virtual figures using this logic. You just know what you are adding, what you are doing while adding, so let’s start...

Step 0.5: Find leisure (Time pass time)

Step   1: First draw/write random numbers, as you did in 1st std while playing Uncles House, (In Marathi, Mamacha Ghar). Don't use higher numbers, we don’t want to add numbers here, we want out brain to learn adding, These two are different things. So just write 1 to 9 random numbers, any no of times.

Step 2: Then put cap on your pen & try adding mentally with following rules

1. Don't say numbers while adding, mentally too, just move tip over different random numbers, add, just add, no matter whether addition is right or wrong
2. Rule : 9 + a = [1][a-1] e.g. 9+7 = [1][7-1] = 16, a's range = {a belongs to  2-10}
3. Rule : 8 + a = [1][a-2] ==> 8+6 = [1][6-2] = 14
4. Rule : 7 + a = double smaller + | 7-a | ==> 7+8 = 7 x 2 + | 7-8 | = 14 + 1 = 15, 7 + 5 = 10 + 2 = 12
5. Design your rules & play with them
6. If you want go infinitely or stop when addition becomes 100, 200, 300 etc.

I have created a random numbers set, see my level of difficulty. b/t/w (By the way) You know, what I did just ? This is great idea for developing mobile app that will help ppl to add fastly, very fastly.

  ...Since you can't use tricks every where....

                                            ----Prof. Vikas Ghode