Same Technique is applied here that we have used for squaring numbers with last digit as 5
**Example 1**

32 X 38 = 12 16

Step 1: Multiply 2 with 8 and write on the right side.

Step 2: Next number to 3 is 4, multiply 4 with 3 and write on the left side.

Answer is 1216

**Example 2**

33 X 37 = 12 21

Step 1: Multiply 3 with 7 and write on the right side.

Step 2: Next number to 3 is 4, multiply 4 with 3 and write on the left side.

Answer is 1221

**Example 2**

62 X 68 = 42 16

Step 1: Multiply 2 with 8 and write on the right side.

Step 2: Next number to 6 is 7, multiply 4 with 3 and write on the left side.

Answer is 4216

Note: when you multiply right side digit 1 with 9, you will write 09

**Exercise**

- 16 X 14
- 12 X 18
- 17 X 13
- 24 X 26
- 22 X 28
- 21 X 29
- 61 X 69
- 62 X 68
- 51 X 59
- 53 X 57
- 106 X 104
- 1003 X 1007
- 1004 X 1006
- 89 X 99
- 789 X 999
- 8977 X 9999
- 43324 X 99999
- 654321 X 999999
- 987 x 999
- 4834 X 9999
- 36 X 999
- 48 X 999
- 9 X 999
- 453 X 99
- 36846 X 999
- 43236 X 9999

Answers: 1. 224 2. 216 3. 221 4. 624 5. 616 6. 609 7. 4209 8. 4216 9. 3009 10. 3021 11. 3021 12. 1010021 13. 1010025

Case 1:

Multiply 654 X 999

Answer: 654 X 999 = 653 346

**Technique:**

Step 1: 654 - 1 = 653 write it on left side.

Step 2: Subtract 653 from 999 999-653= 346 write this on write side.

Answer is 653 346

Case 2:

Multiply 45 X 999

Answer: 044 954
**Technique:**

Step 1: 45 - 1 = 44 write it on left side.

Step 2: Subtract 044 from 999 999-045= 955 write this on write side.

Answer: is 044 954

Case 3:

Multiply 645 X 99

Answer: 645 X 99 = 63855

**Technique:**

Step 1: 645 (100-1)

Step 2: 645 X100 - 645

Step 3: 64500 - 645 = 63855

**Exercise:**

In this technique we will see how to multiply numbers with series of 1's. Thus the multiplier will have numbers like 1, 11, 111, 111 etc.

**Example 1**

Multiply 32 X 11

Answer: 32 X 11 = 352

**Technique:**

Step 1 : First we write the right hand most digit 2 as it is. Answer (----2)

Step 2: Add no 2 to the number in the left 3 and right 5
Answer (-----52)

Step 3 We write the left hand most digit 3 as it is. Answer is (352)

**Example 2**

Multiply 36 X 11

Answer: 36 X 11 = 396

**Technique:**

Step 1 : First we write the right hand most digit 6 as it is. Answer (----6)

Step 2: Add no 6 to the number in the left 3 and right 9
Answer (-----92)

Step 3 We write the left hand most digit 3 as it is. Answer is (396)

**Example 3**

Multiply 74 X 11

Answer: 74 X 11 = 814

**Technique:**

Step 1 : First we write the right hand most digit 4 as it is. Answer (----4)

Step 2: Add no 4 to the number in the left 7 and right 1 and carry 1
Answer (-----12)

Step 3 We write the left hand most digit 7 plus 1( carried over) as 8. Answer is (814)

**Example 4**

Multiply 652 X 11

Answer: 652 X 11 = 7172

**Technique:**

Step 1 : First we write the right hand most digit 2 as it is. Answer (----2)

Step 2: Add no 2 to the number in the left 5 and write 7
Answer (-----72)

Step 3 Add 5 to 6, it come out 11 write 1 in answer and carry 1 Answer (...172)

Step 3 Add 1 carry forwarded to 6 and write in answer. Answer is (7172).
Example 5:

Multiply 3103 X 11
Answer is 34133
**Technique:**

Step 1 : First we write the right hand most digit 3 as it is. Answer (----3)

Step 2: Add no 3 to the number in the left 0 and write 3
Answer (-----33)

Step 3 Add 0 to 1, write 1 in answer is (...133)

Step 4 Add 1 to 3 and write in answer. Answer is (...4133).
Step 4 Write 3 as it is. Answer is (34133)
Example 6:

Multiply 3801375 X 11

Answer is 41815125

**Technique:**

Step 1 : First we write the right hand most digit 5 as it is. Answer (----5)

Step 2: Add no 5 to the number in the left 7 it come 12 and write 2 and carry forward 1
Answer (-----25)

Step 3 Add 7 to 3, it come 10 add 1 carry forwarded now it is 11 write 1 in answer and carry 1 (...125)

Step 4 Add 3 to 1 and add 1 carries and write in answer. Answer is (...5125).

Step 5 Add 1 to 0 and write 1 Answer is (.....15125)

Step 6 Add 0 to 8 and write 8 in answer. answer is (...815125)

Step 7 Add 8 to 3 it comes 11 write 1 and carry 1. Answer is (...1815125)

Step 8 We are o write 3 as it is , but 1 is carried and will be added to 3. Answer is (41815125)

WHEN WE MULTIPLY A NUMBER BY 11 WE WRITE THE LAST DIGIT AS IT IS. THEN MOVE TOWARDS LEFT AND GO ON ADDING TILL WE REACH THE LAST DIGIT AND THE WRITE THE LAST DIGIT AS IT IS OR LAST DIGIT PLUS CARRY FORWARD NUMBER.

** Multiply numbers by 111**

Example 1:

Multiply 203 X 111

Answer: 203 X 111 = 22533

Technique:

Step 1: We write down last digit 3 as it is. Answer is (.........3)

Step 2: Move to left add 3 to 0 and write 3. Answer is (.........33)

Step 3: Move to left add add (2+0+3) - added 3 digits. Answer

(......533)

Step 4: Move to left add (0+2)= 2 Answer is (...2533)

Step 5: We take the last digit 2 as it is (Answer is (22533)

Example 2

Multiply 201432 X 111

Answer : 201432 X 111=22358952

Tecknique:

Step 1: last Digit 2 to be written as it is. write 2

Step 2: We move to left (2+3) and write 5

Step 3: We move to left (2+3+4), write 9

Step 4: We move to left (3+4+1), write 8

Step 4: We move to left (4+1+0), write 5

Step 5: We move to left (1+0+2), write 3

Step 6: We move to left (O+2), write 2

Answer 22358952

THE BEAUTY OF THE TECHNIQUE IS THAT IT CONVERTS THE PROCESS OF MILTIPLICATION TO BASIC ADDITION

Exercise:

111 X 111

2035 X 111

90321 X 111

6021203 X 111

MULTIPLY A NUMBER BY 1111

The only difference will be that we will add maximum four numbers at a time ( There are four one's in 1111)

Example 1

Multiply 210432 by 1111

Answer: 210432 X 1111 = 233789952

Technique: Step 1 We write down the Last Digit as it is - 2

Step 2 Add (2+3)=5 write down - 52

Step 3 Add (2+3+4) = 9 write down -952

Step 4 Add (2+3+4+0) =9 write - 9952

Step 5 Add (3+4+0+1) =8 write - 89952

Step 6 Add (4+0+1+2) =7 write - 789952

Step 7 Add (0+1+2)= 3 write - 3789952

Step 8 Add (1+2) = 3 write - 33789952

Step 9 Write 2 as it is - 233789952

Answer: 210432 X 1111 = 233789952

WHEN THE MULTIPLIER IS 11111 WE WILL BE MULTIPLYING MAXIMUM FIVE DIGITS AT A TIME.

This technique is basically an extenstion of the previous technique.

How to multiply numbers with 2's like 2222 and 3's, like 33, and such other numbers.

Example 1

Multiply 333 X 222

= 333 X 2 X 111

=666 X 111

Now apply the same technique as we were using for 1's.

666 X 111 = 73926

Repeting the technique

Technique:

Step 1: We write down last digit 6 as it is. Answer is (.........6)

Step 2: Move to left add 6 to 6 and write 2 and carry 1. Answer is (.........26)

Step 3: Move to left add add (6+6+6) - added 3 digits it is 18 and add 1 carried - it is 19 write 9 and carry 1 . Answer

(......926)

Step 4: Move to left add (6+6)= 12 add 1 carried- write 3 and carry 1 Answer is (...3926)

Step 5: We take the last digit 6 + 1 carried as it is (Answer is (73926)

Example 2

Multiply 3021 by 333

3021 X 333

=3021 X 3 X111

=9063 X 111

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