free-gmat-downloads_Vedic mathematics1

5 / 12 / 7 = 627

The 1 in 12 is carried over to 5 to give 6

Example 3. Find 234 X 11

234 X 11 is [2 and 2+3 and 3+4 and 4] equals 2 5 7 4

Example 4. Find 777 X 11

777 X 11 is [7 and 7+7 and 7+7 and 7] simplifies to [ 7 and 14 and 14 and 7 ]

7 /14 / 14 / 7 = 8 5 4 7

Answer is 8547. We simply carry the 1's over

Example 5. Find 13423 X 11

13423 X 11 is [1 and 3+1 and 3+4 and 4+2 and 2+3 and 3] simplifies to [1 and 4 and 7 and 6 and 5 and 3]

Answer is 147653

Assignments

Find the Following

Q1. 37 X 11

Q2. 137 X 11

Q3. 12337 X 11

Q4. 567 X 11

Q5. 98 X 11

Assignments Answers

Find the Following

Q1. 407

Q2. 1507

Q3. 135707

Q4. 6237

Q5. 1078

http://www.fastmaths.com

Ch4 : Multiplication

4.9 Multiplication by 12

Multiplication table of 12 is easy to remember

12 X 1 = 12

12 X 2 = 24

12 X 3 = 36

12 X 4 = 48

12 X 5 = 60

12 X 6 = 72

12 X 7 = 84

12 X 8 = 96

12 X 9 = 108

Multiplication of large numbers with 12 is also easy. Just double the digit to the left before adding

Example 1. Find 52 X 12

52 X 12 is

Add 0 to the left and right as shown below

Answer is 624

Example 2. Find 234 X 12

234 X 12 is

Add 0 to the left and right as shown below

Answer is 2808

Example 3. Find 65214 X 12

65214 X 12 is

Add 0 to the left and right as shown below

Answer is 782568

Assignments

Find the Following

Q1. 98 X 12

Q2. 56 X 12

Q3. 134 X 12

Q4. 564 X 12

Q5. 123498 X 12

Assignments Answers

Find the Following

Q1. 1176

Q2. 672

Q3. 1608

Q4. 6768

Q5. 1481976

http://www.fastmaths.com

Ch4 : Multiplication

4.10 Multiplication by vertically and Crosswire

We have seen all the multiplication sums had at least one of the numbers to be multiplied close to a particular base of 10,100 , 1000 etc. We learn a more general formula which can be used for all cases of multiplication.

Multiplying 2 two-digit Numbers

Remember the following diagram. Each dot represents a digit in the number and the lines joining the dots stand for digits to be multiplies

Example 1: Multiply 42 by 13

Step 1. Starting from left, multiply the two left handed most digits vertically. 4 X 1 = 4 and set the answer down underneath as the left most part of the answer.

4 2 X

1 3

---------

4

Step 2. Multiply 4 by 3 and 2 by 1, cross multiplying and add these two answers

together 4 X 3 + 2 X 1 = 14. Set down 4 as the next answer digit and carry the 1 to the left.

42 X

1 3

---------

414

Step 3. Multiply 2 by 3 vertically and set down the answer 6 as the right most answer digit.

42 X

1 3

----------

414 6

Step 4. Add to the carry digit to give the answer 546

This method can be started either from the right or from the left.

Example 2 Find 23 X 72

Step 1. Starting from right, multiply the two right-handed most digits vertically. 3 X 2 = 6 and set the answer down underneath as the right most part of the answer.

---------

6

Step 2. Multiply 2 by 2 and 3 by 7, cross multiplying and add these two answers together 2 X 2 + 3 X 7 = 4 + 21 = 25. Set down 5 as the next answer digit and carry the 2 to the left.

---------

25 6

Step 3. Multiply 2 by 7 vertically and set down the answer 14 as the left most answer digit.

-------------

14 25 6

------------

1 6 5 6

Assignments

Find the Following

Q1. 23 X 12

Q2. 87 X 24

Q3. 63 X 42

Q4. 28 X 98

Q5. 45 X 67

Assignments Answers

Find the Following

Q1. 276

Q2. 2088

Q3. 2646

Q4. 2744

Q5. 3015

http://www.fastmaths.com

Ch4 : Multiplication

4.11 Multiplying larger numbers

Each dot represents a digit in the number and the lines joining the dots stand for digits to be multiplied.

Example 1: Find 362 X 134

Step 1. Starting from left, multiply the two left handed most digits vertically. 3 X 1 = 3 and set the answer down underneath as the left most part of the answer.

Step 2. Multiply 3 by 3 and 6 by 1, cross multiplying and add these two answers together 3 X 3 + 6 X 1 = 15. Set down 5 as the next answer digit and carry the 1 to the left.

Step 3. Middle step is to add the cross product of all six digits as shown below

3 X 4 + 2 X 1 + 6 X 3 = 32

Step 4. Sum of the products of the four right hand most digits give

3 X 2 + 6 X 4 = 30

36 2 X

1 3 4

------------

3 15 32 30

Step 5. The final step is the product of the two right hand most digits 2 X 4 =8

36 2 X

1 3 4

---------------

315 32 30 8

Step 6. After adding up the carry digits the answer is 48508

Example 2 Find 498 X 289

Step 1. Starting from left, multiply the two left handed most digits vertically. 4 X 2 = 8 and set the answer down underneath as the left most part of the answer.

------------

8

Step 2. Multiply 4 by 8 and 9 by 2, cross multiplying and add these two answers together 4 X 8 + 9 X 2 = 50. Set down 0 as the next answer digit and carry the 5 to the left.

------------

8 50

Step 3. Middle step is to add the cross product of all six digits as shown below

4 X 9 + 8 X 2 + 9 X 8 = 36+16+72=124 . Set down 4 as the next answer digit and carry the 12 to the left.

------------

8 50 124

Step 4. Sum of the products of the four right hand most digits give

9 X 9 + 8 X 8 = 81 + 64= 145 Set down 5 as the next answer digit and carry the 14 to the left.

Step 5. The final step is the product of the two right hand most digits 8 X 9 =72

Step 6. After adding up the carry digits

13 12 18 12 2

Step 7. After adding up the carry digits the answer is 143922

Assignments

Find the Following

Q1. 147 X 477

Q2. 270 X 131

Q3. 427 X 47

Q4. 353 X 566

Q5. 777 X 220

Assignments Answers

Find the Following

Q1. 70119

Q2. 35370

Q3. 20069

Q4. 199798

Q5. 170940

http://www.fastmaths.com

Chapter 4 : Multiplication

4.12 Multiplication using Average

Consider the following example

Example 1 : Find 29 X 31

Since the average of 29 and 31 is 30

Find 302 and subtract the square of the difference of either number from the average. 900 - 1 = 899

Square the average and subtract the square of the difference of either number from the average.

Example 2 : Find 26 X 34

Since the average of 26 and 34 is 30

Find 302 and subtract the square of the difference of either number from the average. 900 - 42 = 884

Assignments

Q1. Find 58 X 62 ?

Q2. Find 67 X 69 ?

Q3. Find 98 X 102 ?

Q4. Find 49 X 51 ?

Q5. Find 73 X 93 ?

Assignments Answers