free-gmat-downloads_Vedic mathematics1
.pdf
Find the following |
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Q1. 9 X 13 |
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Q2. 8 X 17 |
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Q3. 97 |
X 106 |
Q4. 88 |
X 102 |
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Q5. 997 |
X 1006 |
Q6. 989 |
X 1028 |
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Assignments Answers
Find the following
Q1. 9 X 13 = 117 |
Q2. 8 X 17 = 136 |
Q3. 97 X 106 =10282 |
Q4. 88 X 102 = 789888 |
Q5. 997 X 1006 = 1002982 |
Q6. 989 X 1028 = 1016692 |
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www.fastmaths.com
Ch4 : Multiplication
4.3 Squaring numbers that ends in 5
Example 1 : Find 75 2
75 X
75
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8X7 / 5X5 |
=> 5625 |
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Simply multiply 7 the number before 5 by the next number up 8 . This gives 7 X 8 = 56 as the first part of the answer and the last part is 5 X 5 =25 so the answer is 5625
Example 2 : Find 3052
30 5
30 5
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30X31 / 5X5 => 93025
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Simply multiply 30 the number before 5 by the next number up 31 . This gives 30 X 31 = 930 as the first part of the answer and the last part is 5 X 5 =25 so the answer is 93025
Assignments
Find the following |
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Q1. |
352 |
Q2. |
452 |
Q3. |
1052 |
Q4. |
952 |
Assignments Answers
Find the following |
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Q1. |
1225 |
Q2. |
2025 |
Q3. |
11025 |
Q4. |
7225 |
http://www.fastmaths.com
Ch4 : Multiplication
4.4 Multiplying numbers whose first figures are the same and whose last figures add up to 10, 100 etc
Example.1 : Find 43 X 47
Check for R.H.S : 3 + 7 = 10, L.H.S. portion remains the same i.e.,, 4.
4 3 X
4 7
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4X5 / 3X7 => 2021
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Multiply 4 ( the same figure in both the numbers ) by the next number up 5. This gives 4 X 5 = 20 as the first part of the answer and the last part is 3 X 7 = 21 so the answer is 2021
Example.2 : Find 31 X 39
Check for R.H.S : 9 +1 = 10, L.H.S. portion remains the same i.e.,, 3.
31 X
39
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3X4 / 1X9 => 1209
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Multiply 3 ( the same figure in both the numbers ) by 4. This gives 3 X 4 = 12 as the first part of the answer and the last part is 1X 9 = 09 so the answer is 1209
Example.3 : Find 127 X 123
Check for : 7 + 3 = 10, L.H.S. portion remains the same i.e.,, 12.
12 7 X
12 3
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12X13 / 7X3 => 15621
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Answer is 15621
Example.4 : Find 395 X 395
Check for : 5 + 5 = 10, L.H.S. portion remains the same i.e.,, 39.
39 5 X
39 5
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39X40 / 5X5 => 156025
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Answer is 156025
Assignments
Find the following |
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Q1. |
23 X 27 |
Q2. |
34 X 36 |
Q3. |
62 X 68 |
Q4. |
136 X 134 |
Assignments Answers
Find the following |
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Q1. |
621 |
Q2. |
1224 |
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Q3. |
4216 |
Q4. |
18224 |
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http://www.fastmaths.com
Ch4 : Multiplication
4.5 Numbers of which the last 2 0r 3 0r 4 digits added up give 100,1000,10000
The same rule works when the sum of the last 2, last 3, last 4 digits added respectively equal to 100, 1000, 10000 .
Example.1 : Find 292 X 208
Here 92 + 08 = 100, L.H.S portion is same i.e. 2
292 X
208
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2X3 / 92X08 => 60/736
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60 / 736 ( for 100 raise the L.H.S. product by 0 i.e 6X10 )
Answer is 60736.
Example.2 : Find 848 X 852
Here 48 + 52 = 100, L.H.S portion is same i.e. 8
848 X
852
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8X9 / 48X52
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We can use our fastmaths technique to find the product of 48X52
48 |
-2 [ BASE 50 ] |
52 |
2 |
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Half of ( 50) / complement of 04 => (25-1)/ 96 => 2496
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and write 848 x 852 = 8 x 9 / 48 x 52
= 720 / 2496 ( for 100 raise the L.H.S. product by 0 i.e 72X10)
=(720+2)/496 = 722496
Since L.H.S product is to be multiplied by 10 and 2 to be carried over as the base is 100
Answer is 722496
Example.3 : Find 693 X 607
Check for : 93 + 07 = 100, L.H.S. portion remains the same i.e., 6
6 93 X
6 07
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6X7 / 93X07 => 2021
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Now R.H.S product 93 X 07 can be obtained mentally.
693 x 607 = 6 x 7 / 93 x 07
=420 / 651 (for 100 raise the L.H.S. product by
0 i.e. 42X10)
=420651.
Answer is 420651.
Assignments
Find the Following
Q1. 393 X 307
Q2. 696 X 604
Q3. 873 X 827
Q4. 188 X 112
Q5. 454 X 446
Assignments Assignments
Find the Following
Q1. 393 X 307 = 120/651 = 120651
Q2. 696 X 604 = 420384 = 420/384 = 420384 Q3. 873 X 827 = 720/1971 = 721971
Q4. 188 X 112 = 20/1056 = 21056
Q5. 454 X 446 = 200/2484 =202484
http://www.fastmaths.com
Ch4 : Multiplication
4.5 Numbers of which the last 2 0r 3 0r 4 digits added up give 100,1000,10000
The same rule works when the sum of the last 2, last 3, last 4 digits added respectively equal to 100, 1000, 10000 .
Example.1 : Find 292 X 208
Here 92 + 08 = 100, L.H.S portion is same i.e. 2
292 X
208
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2X3 / 92X08 => 60/736
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60 / 736 ( for 100 raise the L.H.S. product by 0 i.e 6X10 )
Answer is 60736.
Example.2 : Find 848 X 852
Here 48 + 52 = 100, L.H.S portion is same i.e. 8
848 X
852
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8X9 / 48X52
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We can use our fastmaths technique to find the product of 48X52
48 |
-2 [ BASE 50 ] |
52 |
2 |
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Half of ( 50) / complement of 04 => (25-1)/ 96 => 2496
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and write 848 x 852 = 8 x 9 / 48 x 52
= 720 / 2496 ( for 100 raise the L.H.S. product by 0 i.e 72X10)
=(720+2)/496 = 722496
Since L.H.S product is to be multiplied by 10 and 2 to be carried over as the base is 100
Answer is 722496
Example.3 : Find 693 X 607
Check for : 93 + 07 = 100, L.H.S. portion remains the same i.e., 6
6 93 X
6 07
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6X7 / 93X07 => 2021
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Now R.H.S product 93 X 07 can be obtained mentally.
693 x 607 = 6 x 7 / 93 x 07
=420 / 651 (for 100 raise the L.H.S. product by
0 i.e. 42X10)
=420651.
Answer is 420651.
Assignments
Find the Following
Q1. 393 X 307
Q2. 696 X 604
Q3. 873 X 827
Q4. 188 X 112
Q5. 454 X 446
Assignments Assignments
Find the Following
Q1. 393 X 307 = 120/651 = 120651
Q2. 696 X 604 = 420384 = 420/384 = 420384 Q3. 873 X 827 = 720/1971 = 721971
Q4. 188 X 112 = 20/1056 = 21056
Q5. 454 X 446 = 200/2484 =202484
http://www.fastmaths.com
Ch4 : Multiplication
4.6 Multiplication using other bases
Example.1 : Find 568 X 998
Base is 1000
Complement of 568 is 432
Complement of 998 is 002.
568 -432 [ BASE 1000 ]
998 -002
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568 - 2 / 864 => 566 / 864
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Answer is 566864
Example.2 : Find 213 X 203
Base is 200
Complement of 213 is 13
Complement of 203 is 03.
213 13 [ BASE 200 ]
203 03
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213+3 / 39 => 216 x 2 / 39
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since the base is 200 i e 2X100
The numbers are close to 200 which is 100X 2 we multiply only the left hand part of the answer by 2 to get 43239
Answer is 43239
Example.3 : Find 29 X 28
Base is 30
Complement of 29 is -1
Complement of 28 is -2.
29 -1 [ BASE 30 ]
28 -2
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29 -2 / 2 => 27 x 3 / 2 since the base is 30 i.e 3X 10
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The numbers are close to 30 which is 10X 3 we multiply only the left hand part of the answer by 3 to get 812
Answer is 812
Example.4 : Find 43 X 44
Base is 40