** Introduction:
**

** * Multiplicand:** The number in which multiplication is called is called multiplication.

*** Multiplier:** The number that is multiplied is called multiplier.

*** Multiplication: **The multiplication multiplier multiplies in multiplication is the result which is called the product. Hence multiplication multiplier = multiplication

** Example: **215 × 20 = 4300

** The short-cut method of multiplication can be divided into two parts.
**

** 1. General Rules:** By this method, the product of all types of numbers can be extracted.

** Noble Suggestion:** More questions about simplification related to the Bank Clerical exams are asked. Multiplication is very important in solving such questions. Therefore, in order to solve more questions in less time, it is very important to adopt the multiplication of Short-Cut Methods to get the product of numbers to 1-30 Also remember the hill ( Table ) so that they can multiply quickly.

**TYPE-1: Multiplication of two, two-digit numbers: **

** TRICK:
General Form: **AB × CD =?

1st Step.

2nd Step.

Last Step.

** Example: **42 × 56 =?

** Explanation:
1st Step. **(2 × 6) = 12 ⇒

2nd Step.

Last Step.

Expected product =

** TYPE-2: Multiplication of two, three-digit numbers:
**

**TRICK:
**

1st Step.

2nd Step.

3rd Step.

4th Step.

Last Step.

** Example: **346 × 527 =?**
Explanation:
1st Step. **6 × 7 = 42 ⇒

**Note:** Here are 4, 4, 5 and 2 numbers obtained from 42, 40, 59 and 26, respectively.

** Exercise – Solve them by TRICK –
(1) **234 × 567 =?

(2)

(3)

(4)

(5)

** TYPE-3: Multiplication of two, four-digit numbers: **

** TRICK: **

** General Form: **ABCD × EFGH =?**
Working Steps:
1st Step. **D × H

2nd Step.

3rd Step.

4th Step.

5th Step.

6th Step.

Last Step.

** Example: **5314 × 6272 =?

** Explanation: 1st Step.** 4 × 2 = 8**
2nd Step. **1 × 2 + 4 × 7 = 30 ⇒

3rd Step.

4th Step.

5th Step.

6th Step.

Last Step.

Expected product

** Note: **Similarly, the product of five and six digit numbers can also be known.

** TYPE-4: Multiplication of two numbers of different lengths: **

** 1. **If any number of three digits is to be multiplied by any other number, then the number of three digits is created by placing a zero (0) on the left of the two digit number and three Multiplication by the number of points multiplied by the number of three digits is obtained.

** 2. **If a number of four digits is to be multiplied by any other number of three digits, then the number of four digits is created by placing a zero (0) on the left of the three digit number and four Multiplication is done by multiplying the number of digits by the number of four digits.

** Example 1. **753 × 46 =?**
Explanation: 1st Step. **3 × 6 = 18 ⇒

2nd Step.

3rd Step.

Last Step.

Expected product =

**Example 2. **4326 × 532 =?

2nd Step.

3rd Step.

4th Step.

5th Step.

Last Step.

** Exercise – Solve them by TRICK
(1) **367 × 56 =?

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

** TYPE-5 **

** Multiplication in a Certain Number by Any Number from 11 to 19: **

** TRICK: **To multiply any number from 11 to 19 in any multiplication multiplied by the multiplier of each of that multiplication multiplication is obtained.

** Example: **34526 × 13 =?

** Explanation: 1st Step.** 6 × 13 = 78 ⇒ _{ 7}8**
2nd Step. **2 × 13 = 26 ⇒

3rd Step.

4th Step.

Last Step.

Therefore, the desired product = 39_{5}2_{6}5_{2}6_{7}8 = 448838 **Answer. **

** Exercise – Solve them by TRICK
(1) **4153 × 11 =?

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

** Section-A **

** Specialty of Multiplication on Whole Numbers: **

** TYPE-1 same and Ten rules: **

If the product of such two numbers is to be known, whose sum of digits is ’10’ and the remaining numbers are equal, then by multiplying the digits of the unit by multiplying both points (if the product comes in one digit, just before it) A zero ‘(0) is completed and two digits are completed) on the right side is placed and by adding “1” in the same number, multiplying the number with the same number, Keeping the right (left) on the right, the product of these numbers gets achieved.

(Here x is the same number and y and z respectively are the units of the unit of both numbers)

** Example: **86 × 84 =?**
Explanation: **86 × 84 = 8 × (8 + 1) / 6 × 4 = 7224

** Exercise – Solve them by TRICK
(1) **35 × 35 =?

(2)

(3)

(4)

(5)

** TYPE 2
Same and Five Rule **

If the product of two numbers is to be known, whose unit digits have the sum ‘5’ and the remaining numbers are equal, then the number of points of the unit is folded by the left and the left side of the given product is given a zero (0). After that, by adding a ‘1/2’ part of the same number of squared by the square of the same number, the number of those numbers gets obtained by keeping the number obtained before zero (‘0’). Thus multiplication =

(Here x is the same number and y and z respectively are unit numbers of both numbers.)

**Note: **If ‘1/2’ is in the sum of the ‘class’ + ‘1/2’ part of the same number, then ‘5’ in the zero at the position of ‘ten’ for the ‘1/2’ are given.

**TYPE 3 Ten and Same Rule **

** TRICK – **If the two numbers of units whose units are identical and the sum of the tenth digit is 10, then the two digits of the number obtained by the square of the digits of the unit (if the same digit If the same number is received after the class, then a zero (0) is placed on the left side of its left side, and the number of points of the tenth digit is added to the number obtained by both the digits Right left is the product of these numbers to put aside.

Thus, the product = y × z + x / x ^{ 2} (Here y and z are respectively ten and digit of first and second numbers and 2 units have the same number)

**TYPE 4: Five and Same Rule**

** TRICK: **If the number of two numbers is identical to the one whose unit is the same number and the sum of the tenth digit is ‘5’ then the two digits of the number obtained by the square of the same number of units If the same number is obtained after classing the same digit, then a zero (‘0’ is placed on its left side) is placed on the right side and in the product of tens digits, half of the unit number ‘1/2’ is added Those two Shall also be the product of these numbers to keep the right to the left of the numbers.

Thus multiplication =

(Here y and z is the number of tenths of first and second numbers respectively)

** Note: **1/2 = 10/2 = 5, that is, 5 for ½ is added to the number 4 on the right.

**TYPE-5
Same and Twenty Rule **

** TRICK – **If the last two digits of multiplication and the last two digits of multiplication are 20 and the remaining numbers are equal, then the last two digits of multiplication and the four digits of the product of the last two digits of multiplication If not in the four digits, the left digit is filled with zero (0) and it is placed on the right side and add 1/5 of the same number in the same number of squares and place them on the right hand side.

Giving these numbers the product of these numbers is achieved. Thus multiplication =

(Here x is the same number and y and z are respectively two-two digits of multiplication and multiplication.)

** Note: **1/5 = 10/5 = 2, that is, 2 for 1/5, the points on the right are added to zero (0).

** Exercise – Solve them by TRICK
(1) **4506 × 4514 =?

(2)

(3)

(4)

(5)

** TYPE-6 Same and Forty Rule: **

** TRICK – **If the sum of the multiplicity and the multiplier is equal to 40, and the remaining numbers are equal, then the four points of multiplication of the multiplicity and multiplication of the two two points (if the product is not in four digits On the left side, the fourth digit is completed by sitting at zero (0), it is placed on the right side and by adding 2/5 of the same number in the same number of squares, keeping them on the right side, the product of these numbers Will be received The breakfast. Thus multiplication =

(Here C is the same number and y and z are respectively two to two digits of multiplication and multiplication.)

** Note: **4/5 = 40/5 = 8 that is equal to 8/4, 8 is added to zero (0) on the right side.

** Exercise – Solve them by TRICK –
(1) **5523 × 5517 =?

(2)

(3)

(4)

(5)

** TYPE – 7 Same and Fifty Rule **

** TRICK: **If the sum of the multiplicity and the multiplier is equal to 50, and the remaining numbers are equal, then the four points of multiplication of multiplication and multiplication of multiplication and multiplication (if the product is not in four digits If you come to the left, four digits are completed by sitting on the right side), the right is placed on the right side and by adding ‘1/2’ part of the same number to the same number of classes, the product of these numbers is obtained by writing them on the right hand side. Have It goes.

Thus multiplication =

(Here x is the same number and y and z are respectively two to two digits of multiplication and multiplication.)

** Note: **1/2 = 10/2 = 5, that is, 5 for ½ is added to the numerator on the right.

** Exercise – Solve them by TRICK –
(1)** 4032 × 4018 =?

(2)

(3)

(4)

(5)

** TYPE-8 Same and Sixty Rule:
**

Thus multiplication =

(Here x is the same number and y and z are respectively two to two digits of multiplication and multiplication.)

** Note: **1/5 = 10/5 = 2 that is equal to 2 for 1/5, the number on the right side is added to zero (0).

** TYPE-9 Same and Eighty Rule **

** TRICK – **If the sum of the two digits of multiplication and multiplication is ’80, and the remaining numbers are equal, then the four points of multiplication of the multiplicity and the multiplication of the two two points (if the product is in four digits If not, then ‘4’ is done by sitting ‘0’ on the left hand side.) Is placed on the right side and after adding 4/5 of the same number to the same number of classes, the product of that number gets.

Hence product =

(Here x is the same number and y and z are respectively two-two digits of multiplication and multiplier)& nbsp;

** Note : **3/5 = 30/5 = 6 that is, 6 for 3/5 is added to the number 1 on the right side.

** Exercise – Solve them by TRICK
(1) **565 × 515 =?

(2)

(3)

(4)

(5)

** TYPE – 10 Same and Hundred Rule
**

Thus, the product = x

(Here x is the same number and y and z are respectively two-two digits of multiplication and multiplication.)

**Exercise Solve them by TRICK**

** (1) **1773 × 1727 =?**
(2) **2956 × 2944 =?

(3)

(4)

(5)

** Section-B **

** Multiplication of any number by Repeated Digit Numbers **

** TYPE-1
TRICK: **If the number of four digits is to be multiplied by ’11’, then the sum of the digits of the unit number, unit and tenth digit of the number, the sum of the tens and the hundredths, the hundredth and the thousand The sum of the digits and finally the thousand points are placed at the place of unit, ten, hundredth, thousand and ten thousand, respectively for product, as well as the addition is added to their left.

Note:

** Example 1. **2346 × 11 =?**
Explanation: 1st Step. **= 6

2nd Step.

Therefore, the desired product = 257

** Example 2. **4327 x 111 =?**
Explanation : 1st Step. **= 7

2nd Step.

3rd Step.

Therefore, the desired product = 479

** Example 3. **53148 × 1111 =?**
Explanation: 1st Step. **8

2nd Step.

Therefore, the desired product is 589

** Example 4. **734 × 1111 =?**
Explanation: **? = 0734 × 1111

1st Step.

2nd Step.

3rd Step.

Expected Product = 7_{1}0_{1}4_{1}474 = 815474 ** Answer **

** Exercise – Solve them by TRICK –
(1) **234 × 11 =?

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

** TYPE-2 Multiplication By Repeated digit 2 to 8 Numbers **

** TRICK: **If a four-digit number is to be multiplied by 222, then the sum of the digits of the unit of that number, the sum of the units and the tens, the sum of the digits, the tens, and the sum of the digits, the tens, The number of hundred and sixty thousand digits and multiplying the number of thousand by 2 is multiplied by the number of units, ten, hundredth, thousandth, ten thousand and lakhs respectively. At the same time, gain is added to your left hand.**
Note:
(i) **If the multiplier is two, four or five digits then the sum of the maximum digits will be two, four and five digits, respectively.

** Example 1.** 6324 × 222 =?**
Explanation:
1st Step. **4 × 2 = 8

2nd Step.

3rd Step.

4th Step.

5th Step.

Last Step.

** Example 2. **234 × 33 =?**
Explanation: 1st Step. **4 × 3 = 12 ⇒

2nd Step. (3 + 4) × 3 = 21 ⇒ 21

3rd Step. (2 + 3) × 3 = 15 ⇒

Last Step. 2 × 3 = 6

Expected product = 6

** Example 3. **1231 × 6666 =?**
Explanation: 1st Step. **1 × 6 = 6

2nd Step.

Therefore, the desired product = 6

** Note: **If the number of points of multiplication is less than the number of digits of the multiplier, then by placing zero (0) on the left side of the multiplication, the number of points of the multiplier is equalized and obtained the product as per above rule goes.

** Example 4. **432 × 88888 =?**
Explanation: **? = 00432 × 88888 = …

1st Step.

Therefore, the desired product = 32

** Exercise – Solve them by TRICK –
(1) **326 × 22 =?

(2)

(3)

(4)

(5)

(6)

(7)

(8)

**Section-C **

** Multiplication of two Numbers in the Neighborhood of 100
TYPE-1 **

** TRICK – **If both multiples and multipliers are less than 100 numbers, then the numbers of two numbers will be less than 100, by multiplying those deficiencies, two points of the received number are placed on the right for the product and the first number By decreasing the number of second number, the received number is placed on the left side for the product.

**Note:** If the product of the weaknesses comes in one digit, then two digits are completed by placing zero (0) on the left and if the product comes in three digits then one digit on its left is achieved.

** Example 1. **96 × 92 =?**
Explanation: **? = 96 – 8/4 × 8 = 88/32 = 8832 [“100-96” = 4 and “100-92” = 4]

** Example 2. **83 × 87 =?**
Explanation: **? = 83 – 13/17 × 13 = 70/21 = 7221 Ans. [“100-83” = 17 and “100-87” = 13)

** Example 3. **96 × 98 =?**
Explanation: **? = 96 – 2/4 x 2 = 94/08 = 9408 Ans. [“100-96” = 4 and “100 – 98” = 2]

** TYPE -2 **

** TRICK: **If multiples and multipliers are both numbers greater than 100, then the two numbers will be more than 100, by multiplying the increments, two points of the given product are placed on the right for the product of the given numbers. And the number obtained by adding the second number increment in the first number is placed on the left for the product.**
Note: **If the product of the increment comes in one point, then the remaining two digits are completed by sitting in the zero (0). If the product comes in three digits then one end of the left is taken.

** Example 1. **107 × 109 =?**
Explanation: **? = 107 + 9/7 × 9 = 116/63 = 11663 Answer.

** Example 2 **103 × 102 =?**
Explanation: **? = 103 + 2/3 × 2 = 105/06 = 10506 Answer.

** TYPE -3 **

** TRICK – **If one of the multiples and multiples is less than 100 and the second number is greater than 100, then if the numbers increase or decrease by 100 in the two numbers, then multiply both of those The two digits are taken from one digit to the left by the number of 100 and placed on the right for the product of the given numbers, and by adding the second number increment in the first number or decreasing it from that number One at Key is placed on the right to the product of those numbers.

** Example 1. **93 x 108 =?? = 93 + 8/7 × 8 = 101/56 = 100 / (100 – 56) = 10044 Answer.

Explanation:

** Example 2. **86 × 109 =?**
Explanation: **? = 86+ 9/14 × 9 = 95/126 = 93 / (200-126) = 93/74 – 9374 Αns.

** Note: **is 100 to 126 more. Therefore, from the left side, 2 out of 200 is reduced to 126.

** Exercise – Resolve it with Trick.
(1) **92 × 97 =?

(2)

(3)

(4)

(5)

** Multiplication of Two Numbers in the Neighborhood of 1000:
**

** Note: **In multiplication and multiplication, if one number is less than 1000 and the second number is larger then by decreasing the decrease and the increase, the three digits of the product obtained are subtracted from 1000 and placed on the right side for the product.

** Example 1. **994 × 991 =?**
Explanation : **? = 994 – 9/6 × 9 = 985/054 = 985054 Answer.

** Example 2. **1012 × 1019 =?**
Explanation: **? = 1012 + 19/12 × 19 = 1031/228 = 1031228 Answer.

** Example 3. **982 × 1014 =?**
Explanation: **? = 982 + 14/18 × 14 = 996/252

= 995 / (1000-252) = 995/748 = 995,748 Answer.

** Exercise – Solve them by TRICK –
(1) **986 × 983 =?

(2)

(3)

(4)

(5)

** Multiplication of Two Numbers in the Neighborhood of 50 **

** TRICK – **If multiplication and multiplication both numbers are less than or equal to 50, the number of the given numbers of two numbers given by multiplying that growth or deficiency by both numbers will be more or less than 50 To the right. After this the growth of the second number in the first number is added or the reduction is reduced. Thus by dividing the received number from 2, the quotient is placed on the left for the product of numbers.

** Note : **For 1/2 = 10/2 = 5 that is 1/2, 5 is added to the number 2 on the right.

**Exercise :
(1)** 57 × 56 =?

(2)

(3)

(4)

(5)

**Section-D **

** Multiplication. By 5, 25, 125 and 625 **

** TRICK – **If a number is to be multiplied by 5, 25, 125 or 625, then by sitting one, two, three or four zeros on the right side of that number, respectively 2,4, 8 or Participation by 16 gets multiplication.

** Example 1. **4326 × 5 =?**
Explanation: **? = 4326 × 5 = 43260/2 = 21630 Answer.

** Example 2. **53624 × 25 =?**
Explanation : **? = 53624 × 25 = 5362400/4 = 1340600 Answer.

** Example 3. **6237 × 125 =?**
Explanation : **? = 6237000/8 = 779625 Answer.

** Example 4. **732 × 625 =?**
Explanation : **? = 7320000/16 = 457500 Answer.

** Exercise – Resolve it with Trick.
(1) **7354 × 5 =?

(2)

(3)

(4)

(5)

** Multiplication By 75: **

** TRICK – **If any number is to be multiplied by 75, then on the right side of that number, multiplying three by zero and multiplying it by 4 divided by 4 gives the product.

** Example: **3467 × 75 =?

** Explanation: **? = 3467 × 75 = 3 × 349799 = 3 × 86675 = 260025 Answer.

** Unit digit 5 and the difference 10 rule **

** TRICK – **If the number of two numbers is to be known, whose unit’s digit is 5 and its difference is 10, then the right and 76 are written for the product of those numbers and the number of units of both numbers is 5 In addition to the number which is larger, the number which is larger, by adding 1, by multiplying it by the other remaining number, the product obtained is left to the left for the product of those numbers.

** Example : **125 × 135 =?**
Explanation : **? = 125 × 135 = 12 × (13 + 1) / 75

= 156/75 = 15675. Answer.

** Exercise – Solve them by TRICK –
(1) **4265 × 75 =?

(2)

(3)

(4)

(5)

**Section – E **

** General Rules of Multiplication on Mixed Numbers **

** TYPE-1 integral and fractional rules of both Rules **

**TYPE-2: Integral parts same and Fractional Parts Different Rule **

**TYPE-3: Integral Parts Different and Fractional Parts same Rule **

** Special Rules of Multiplication on Mixed Numbers **

** TYPE-1 Same and One rule: **

** TRICK: **If two of the Mixed Numbers are to be known to the product whose sum of Fractional Parts is 1 and the Integral Part is equal, then by multiplying Fractional Parts for the product of those numbers, the product gets written on the right And by adding 1 to one of the equal integral part, multiplying the number by equal number, the product is written on the left side.

** TYPE-2 Same and Half Rule: **

** TRICK – **If the product of two Mixed Numbers is to be known, whose sum of Fractional Parts is ½ and the integral part is equal, then by multiplying Fractional Parts for the product of those numbers, the product gets written on the right side And the sum obtained by adding half of it in the square of one of the same integral part is written on the left for the product of those numbers.

** Note: **If the sum of the fractional part is 1/3, 1/4, 1/8, 1/16 … and so on in the square of the same Integral part, that integral part is 1/3 1 / 4 1/8 1/16 … is added by multiplying it, and this received sum is written on the left.

**Multiplication of Mixed Numbers By whole Numbers: **

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