Multiplications |

A non-mathematical background candidates are also can early solve the multiplications problems with speed and accuracy by following the methods.

**Multiplications shortcut methods:**

Numbers ending with 1

Numbers beginning with 1

Multiplication with 11 number

Multiplication with 25 number

Multiplication with 125 number

Multiplication with 2 digit number

Multiplication -checking answer is correct or incorrect

Multiplication - Missing number

Multiplication -Addition

Decimal -Multiplication

Decimal - Multiplication and additions

Checking of multiplication whether the answer is correct or not, Finding the missing numbers in the multiplication with additions. Decimals multiplication, Decimal multiplication with additions.

Multiplications with ending Number 1

Example-I:

41 x 31 =1271 1 x 1 = 1

1 x 3 + 1 x 4=7

3 x 4 =12

More examples:

51 x 41 = 2091

61 x 71 = 4331

81 x 51 = 4131

Explanation from the above example:

41 x 31 = ?

Step-I: 41 x 31 =____1

Do the Multiplication of the last digit of the second number with the last digit of the first number. The Answer is 1 x 1=1. Write 1 as final answer digit

Step-II: 41 x 31 = __71

Do the Multiplication of cross numbers as the second digit of the second number with the second digit of the first number and add the both results. 1 x 3 + 1 x 4 = 7

Step-III: 41 x 31 = 1271

Do the Multiplication of the second digit of the second number with the second digit of the first number. The answer is 3 x 4 = 12.

Write the final answer

*.*__1271__Example-II: Three digits with two digits multiplication

456 x 31 = 14136

Step-I:____6

Do the multiplication of the last digit of the second number with the last digit of the first number

1 x 6 = 6

Write 6 as final answer digit.

Step-II:___36

Do the cross multiplication of the last digit of the second number with the second digit of the first number and the second digit of the second number with the last digit of the first number. Add both the result. and write as the final result of the second digit.

1x 5 = 5

3 x 6 = 18

Adding both results 5 + 18 = 23

**Write 3 as the second digit of the final result and remember 2 for further calculation.**

__Note:__Step-III:__136

Do the multiplication of the last digit of the second number with the first digit of the first number and multiply the second digit of the second number with the second digit of the first number.

**.**

*Add both answers along with 2 (reminder)*1 x 4 = 4

3 x 5 = 15

Adding results 4 + 15 = 19

= 19 + 2 (reminder)

= 21

Write 1 as final result third digit. Remember 2 in mind for further calculations.

Step-IV:

__14136__

Do the multiplication of the second number of the second digit with the first number of the third digit. Add the both results along with reminder 2. Wire the result as final digits.

3 x 4 = 12

= 12 + 2 (Reminder)

= 14

The final answer is 14136

Example-III: Cross Multiplication of two digit number

47 x 31 = ?

Step-I: ___7

Do multiplication of the last digit of the second number with the last digit of the first number.

1 x 7 = 7. Write answer 7 as the final result last digit.

Step-II: __57

Do multiplication of the last digit of the second number with the first digit of the first number and multiply the second digit of the last number with the second digit of the first number. Add both the results.

1 x 4 = 4

3 x 7 = 21

Add both results 4 + 21 = 25.

In this result write 5 as the final result as the second digit and remember 2 in mind for further calculation.

Step-III: 1457

Do multiplication of the second digit fo the second number with the second digit of the first number. Add the result with 2 (reminder)

3 x 4 = 12

= 12 + 2 (reminder)

= 14

Write 14 as final result.

The final result is 1457

**More shortcut methods follow**

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