Mix 6

DO 9999999×123456 IN SECONDS

        9999999
  ×      123456
_________________
1234559876544


IN SUPPLEMENT TO PREVIOUS POST
WHERE SEVEN TIMES 9 IS MULTIPLIED
BY 7 DIGIT ANY NUMBER.HERE WE ARE
MULTIPLYING 7 TIMES 9 WITH 6DIGIT ANY
NUMBER.
STEPS
1) WRITE 5 DIGIT OF THE 6DIGIT NUMBER AS
    IT IS LIKE 12345 IN THIS EXAMPLE.
2) SUBTRACT 1 FROM 6
    ie 6-1=5
    PUT 5 ALONG WITH 5 NUMBERS
    THUS FIRST PART OF ANSWER IS
    123455
3)NOW SUBTRACT EACH NUMBER
    OF FIRST PART FROM 9 .
    SEVENTH DIGIT  WILL BE
    9.
Explanation
  Write first part of answer as 123455
 Then put 9; thus first part of answer
becomes 1234559
 Then subtract each digit from 9 as
 9-1=8
 9-2=7
 9-3=6
 9-4=5
 9-5=4
 9-5=4

 SECOND PART OF ANSWER = 876544

4) THUS OUR ANSWER IS
     1234559876544


DO THE 7×7 MULTIPLICATION IN SECONDS (MAGICAL TRICK OF 9 )

      9 9 9 9 9 9 9
  ×  2 3 4 5 6 7 8
__________________
23456777654322

STEPS
1) SUBTRACT 1 FROM UNITS PLACE NUMBER
     HERE 8
     8-1=7
2) REPEAT THE SAME NUMBER EXCEPT LAST
    DIGIT;PUT 7 INSTEAD OF 8.
3) WE HAVE STARTING PART OF ANSWER
    ie. 2345677.
4) NOW SUBTRACT 1 FROM EACH NUMBER
    STARTING FROM 2
     eg 9-2 =7
           9-3=6
           9-4=5
           9-5=4
           9-6=3
           9-7=2
           9-7=2
5) NOW WE ARE READY WITH SECOND PART OF ANSWER
    ie.7654322
6) FINAL ANSWER
   23456777654322


3×3 MULTIPLICATION

        1 2 1
    ×  2 3 1
____________
      27951

STEPS
1) MULTIPLY 1×1=1; WRITE IT AT UNITS PLACE.
2) MULTIPLY 1×2=2 & 3×1=3
3)ADD 2+3=5;PUT IT AT TENS PLACE.
4)MULTIPLY 1×1=1;3×2=6 & 2×1=2
5)ADD1+6+2=9;PUT IT AT HUNDREDS PLACE.
6)MULTIPLY 3×1=3 & 2×2=4
7)ADD 3+4=7;PUT IT AT THOUSANDS PLACE.
8)MULTIPLY 2×1=2;PUT IT AT TEN THOUSANDS PLACE.
9)THIS HOW WE GET 27951 IN ONE STEP.
 
   

4×4 MULTIPLICATION

              1 2 2 1
           × 1 1 2 2
         ____________
           1,369,962

STEPS
1) MULTIPLY 2×1=2;PUT IT AT UNITS PLACE.
2) MULTIPLY 2×2=4 & 2×1=2
3) ADD 4+2=6; PUT IT AT TENS PLACE.
4)MULTIPLY 2×2=4;2×2=4;1×1=1
5)ADD 4+4+1=9;PUT IT AT HUNDREDS PLACE.
6)MULTIPLY 2×1=2; 2×2=4;1×2=2;1×1=1
7)ADD 2+4+2+1=9; PUT IT AT THOUSANDS PLACE.
8)2×1=2; 1×2=2;1×2=2
9)ADD 2+2+2=6;PUT IT AT TEN THOUSANDS PLACE.
10)MULTIPLY 1×1=1 & 1×2=2
11)ADD 1+2=3;PUT IT AT LAKHS PLACE.
12)MULTIPLY 1×1=1;WRITE IT AT TEN LAKHS PLACE.
13)WE HAVE 1,369,962 IN ONE LINE.
 
     NOW DO THE 4× 4 MULTIPLICATION ON ONE LINE.

RECALL TABLE UPTO 100 WHENEVER REQUIRED


MAKING TABLE FROM 11 TO 100 IS VERY EASY & CAN BE CALCULATED AT ANY MOMENT.

STEPS :

TABLE OF 23

1 ) WRITE THE TABLE OF 2 & WRITE THE TABLE OF 3 AS BELOW

     
 A
B
 2
0
3
4
0
6
6
0
9
8
1
2
10
1
5
12
1
8
14
2
1
16
2
4
18
2
7
20
3
0

MAKE TWO  COLUMNS AS A & B
IN  FIRST COLUMN 0F 'A'  WRITE  THE  TABLE OF 2
IN SECOND COLUMN OF 'A' WRITE THE TEN'S PLACE OF TABLE 3
IN COLUMN 'B' WRITE THE UNIT'S  PLACE OF TABLE 3

2) NOW, ADD TWO COLUMN OF 'A'  AS BELOW


 A
TOTAL
 2
0
2
4
0
4
6
0
6
8
1
9
10
1
11
12
1
13
14
2
16
16
2
18
18
2
20
20
3
23


3) CLUB 'TOTAL' COLUMN ABOVE & COLUMN ' B ' AS BELOW & TABLE IS READY


TOTAL
B
TABLE
2
3
23
4
6
46
6
9
69
9
2
92
11
5
115
13
8
138
16
1
161
18
4
184
20
7
207
23
0
230

IN THIS WAY YOU CAN CALCULATE MANY MORE TABLE WHENEVER REQUIRED

Test for divisibility of a number by 7 - Vedic Technique

Introduction:
This article will demonstrate how to verify if a numbver is divisible by 7 or not. It will demonstrate using simple vedic ways so that any student, teacher or maths lover can learn it easily.

Testing technique:
1. Double the last digit of the number.
2. Subtract it from the remaining number.
3. Then test the remainder if divisible by 7.
4. If remainder is a large number, repeat steps 1 to 3 again and again till you get a simple number that you can test mentally.

Example:
Let's test 791 to find if it is divisible by 7 or not.
step 1: Lat digit is 1 X 2 = 2
step 2: Remaining number 79 - 2 = 77
step 3: We can say easily that 77 is divisible by 7
Hence, 791 is dividible by 7

Let's test a bit complex number:
7856492

Step 1: 2 X 2 =4
Step 2: 785649 - 4 = 785645 (this is a big number. Repeat step 1 and 2 now)
Step 3: 5 X 2 = 10
Step 4: 78564 - 10 = 78554
Step 5: 4 X 2 = 8
Step 6: 7855 - 8 = 7847
Step 7: 7 X 2 = 14
Step 8: 784 - 14 = 770

Now, easily we can say that 770 is divisible by 7.
Hence the whole complex number 7856492 is divisible by 7.

Vedic Mathematics - Finding Square of a number made easy

Find Square Of a number with Simple and faster Vedic Ways:
Vedic mathematic contains a lot of formulae (Sutra) that not only allows us to do calculations without pen and paper, it also makes our brain to act faster. Now-a-days, to crack in a competitive exam, we must look into two factors, they are SPEED and ACCURACY. By learning Vedic mathematics, one can achieve these two important factors to crack in any competitive exam.

This document contains formulae for finding out square of a number accurately without pen and paper. The formulae are easy to understand and are demonstrated in easy manner with examples.

1. Find Square of a number ending with 5:

1.1 Example: Let’s find out square of 25. a. Break the number to two parts with 2 as first part and 5 as second part
b. Find multiplication of 2 and (2+1), i.e 2 x 3 = 6
c. Find square of 5, i.e. 25
d. Hence, our answer, 25² = 6 25=625
1.2 Lets take another example, i.e. 65 a. 65 = 6 5
b. 6 x (6+1) = 42
c. Square of 5 = 25
d. Hence, 65² = 42 25 = 4225

1.3 Let’s take a 3 digit number, i.e. 125
a. 125 = 12 5
b. 12 x (12 + 1) = 156
c. Square of 5 = 25
d. Hence, 125² = 156 25 = 15625
This way this rule can be used to calculate square of numbers ending with 5 without help of pen and paper.

2. Find Square of a number which is adjacent to a number that ends with 0 or 5:

We can easily find out square of a number that ends with 0 or 5, e.g. 10, 15, 20, 25, 30 etc.
Now we will see how to find out square of an adjacent number like 11, 9, 16, 14, 21, 19 etc
2.1 Example: Let’s find out square of 31.
a. We know square of 30, i.e. 30² = 900
b. Now, 31² = 30² + (30 + 31) = 900 + 61 = 961

2.2 Lets find out square of 46
a. 45² = 2025
b. 46² = 45² + (45 + 46) = 2025 + 91 = 2116

2.3 Lets find out square of 71
a. 70² =4900
b. 71² = 70² + (70 + 71) = 4900 + 141 = 5041
Now, let’s find out numbers which are 1 less to numbers ending with 5 or 0
2.4 Find square of 14
a. 15² = 225
b. 14² = 15² – (14 + 15) =225 – 29 = 196
2.5 Find square of 29
a. 30² = 900
b. 29² = 30² – (29 + 30) = 900 – 59 = 841

3. Find out Square of a number near 100:

Let’s find out square numbers which are close to 100 and are lesser than 100.
3.1 Find square of 97
a. 97 is 3 less than 100 (i.e. -3)
b. 97² = 97 -3 / 03² = 94 / 09 = 9409 (There should be two digits (09 instead of 9) after ‘/’)
3.2 Find square of 96
a. 96 is 4 less than 100 (i.e. -4)
b. 96² = 96 -4 / 04² = 92 / 16 = 9216
3.3 Find square of 87
a. 87 is 13 less than 100 (i.e. -13)
b. 87² = 87 -13 / 13² = 74 / 169 =7569 (There should be two digits(69 out of 169), hence 1 is carry forwarded from 169 and added to 4 of 74)

Let’s find out square of numbers which are close to 100 and are greater than 100.
3.4 Find square of 103
a. 103 is 3 greater than 100 (i.e. +3)
b. 103² = 103 +3 / 03² = 106/09 = 10609
3.5 Find square of 107
a. 107 is 7 greater than 100 (i.e. +7)
b. 107² = 107 +7 / 07² = 114 / 49 = 11449
3.6 Find square of 113
a. 113 is 13 greater than 100 (i.e. +13)
b. 113² = 113 +13 / 13² = 126 / 169 = 12769 (1 is carry forwarded from 169)

I hope this material was helpful to you. I will add some more materials on Addition, Multiplication, Subtraction and Division and other formulae related to Algebra once I compile them.


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