Multiplication Tricks - How to Multiply Numbers in mind without calculator

MULTIPLICATION TRICKS

In this post i will explain mental maths tricks to multiply numbers quickly in your head within seconds. By these multiplication tricks you can multiply 2-digit and 3-digit numbers efficiently without calculator. Sometimes it become complicated and lengthy to multiply and we need calculator to solve it. But in examination where calculators are prohibited, we need to solve it manually which results in wastage of lots of time.

Time management is most important part to crack any exam and that's why in this post i will try to explain few multiplication tricks to solve questions within seconds. Before learning multiplication tricks you can learn about fastest methods of addition-subtraction here.

Multiplication by 5

Put a zero at the right end of the number and divide it by 2.

Example: 486258 x 5
Solution: 4862580/2 = 2431290 
 

Multiplication by 9

Put a zero at the right end of number and subtract the original number from it.

Example: 9546814 x 9

Solution: 95468140 - 9546814 = 85921326

Multiplication by 11

 Step 1:  Write the last figure of the multiplicand as the right-hand figure of the answer.

 

 Step 2:  Add each digit of the multiplicand to its neighbor digit at the right hand.

 

 Step 3:  Keep the unit digit and transfer the rest to the left hand digit and repeat step 2.

 

Example: 58942 x 11

Solution: Write it as 058942 x 11

 

Step 1: Last digit of the multiplicand is 2, so write 2 at unit place of the answer figure. 

Write it like this: 058942 x 11 = _ _ _ _ _ (2) 

Step 2: Now add each digit to its neighbor digit at right hand one by one. 

4 + 2 = 6   [ _ _ _ _ (6) (2)] 

9 + 4 = 13 [ _ _ _ (13) (6) (2)]

 

Step 3: Keep the unit digit of 13 which is '3' and transfer rest, which is '1' here to the left hand digit.

8 + 9 + 1 = 18   [   _ _ (⃔18) (3) (6) (2)]

5 + 8 + 1 = 14   [ _ (⃔14) (8) (3) (6) (2)]

5 + 1 = 6           [(6) (4) (8) (3) (6) (2)]

Multiplication by 12

Double each digit in turn starting from rightmost digit and add to its right hand neighbor.
Example: 56824 x 12
Solution: We can write it as 056824 x 12
 Step 1:  Double last digit which is '4' and add to its right hand digit.
4 x 2 + 0 = 8 [Here neighbor digit is 0]
We can write it as: 56824 x 12 = _ _ _ _ _(8)

 Step 2:  Repeat above step with each digit successively.

2 x 2 + 4 = 8            [     _ _ _ _ (8) (8)]

8 x 2 + 2 = 18          [ _ _ _ (18) (8) (8)]

 Step 3:  Keep the unit digit of 18 which is '8' and transfer rest, which is '1' here to the left hand digit.
6 x 2 + 8 + 1 = 21    [    _ _ (1) (8) (8) (8)]
5 x 2 + 6 + 2 = 18    [  _ (8) (1) (8) (8) (8)]
0 x 2 + 5 + 1 = 6      [(6) (8) (1) (8) (8) (8)]

Multiplication by 13

Treble each digit in turn starting from rightmost digit and add to its right hand neighbor. It is same method which we applied in multiplication of 12, the only difference is here we are multiplying each digit by 3.

Multiplication by 25

Put two zeroes at the right of the number and divide it by 4.

Example: 5468234 x 25
Solution: 5468234 x 25 = 546823400/4 = 136705850

Multiplication by 999...

Count the number of nines and place same number of zeros at the end of multiplicand. Subtract the original number from this new number.
Example: 678 x 999
Solution: 678000 – 678 = 677322

Multiplication of Two Digit Numbers

Example: 12 x 13
Solution:  Step 1:  Multiply the rightmost digits (unit digits) of both the numbers.
                   ⇒ 2 x 3 = 6
We can write 12 x 13 as: _ _ (6)

 Step 2:  Now do cross multiplication of all 4 digits and add the product.
        ⇒ 1 x 3 + 1 x 2 = 5
We can write 12 x 13 as: _ (5) (6)

 Step 3:  Multiply the leftmost digits of both the numbers.
        ⇒ 1 x 1 = 1
We can write 12 x 13 as: (1) (5) (6)
Answer will be: 156

 SECOND METHOD 
This method is useful when both the numbers are near to common bases i.e powers of base 10.
Example: 46 x 43
Solution:  Step 1:  Take the nearest common multiple of 10, here we can take 40 as common base and treat it as 4 x 10.

 Step 2:  Write the number like this: 46 is 6 more than common base and 43 is 3 more than common base.

 

Cross addition always gives same result and also multiply the last digits.

 Step 3:  As common base is 4 x 10, so multiply left hand digits with '4' and all digits except '8' will be transferred to left hand digits.
        ⇒ 49 x 4 = 196
        ⇒ 196 ⃔|18 = 1978

We can also write  Step 3  like this: 49 x common base = 49 x 40 = 1960.
Now add left hand digits to it = 1960 + 18 = 1978

The above steps can be done mentally without paper-pen.

Example: 73 x 54
Solution: Here we are taking common base as 60 = 6 x 10

 As right hand digit is negative, subtract it from left hand digits:
        ⇒ 4020 - 78 = 3942

Multiplication of Three Digit Numbers

Example: 213 x 143
Solution:  Step 1:  Multiply the rightmost digits (unit digits) of both the numbers.
                       ⇒ 3 x 3 = 9
Write like this 213 x 143 : _/_/_/_/9

 Step 2:  Now do cross multiplication of right 4 digits and add the product.
          ⇒ 1 x 3 + 3 x 4 = 15
Write like this 213 x 143 : _/_/_/15/9

 Step 3:  Now do cross multiplication of all the digits and add the product.
          ⇒ 2 x 3 + 1 x 4 + 3 x 1 = 13
Write like this 213 x 143 : _/_/13/15/9

 Step 4:  Now do cross multiplication of left 4 digits and add the product.
          ⇒ 2 x 4 + 1 x 1 = 9
Write like this 213 x 143 : _/9/13/15/9

 Step 5:  Multiply the leftmost digits of both the numbers.
          ⇒ 2 x 1 = 2
Write like this 213 x 143 : 2/9/13/15/9

 Step 6:  Now keep the unit digits and transfer rest to the left digits and add them.
          ⇒ 2/9/⃔13/⃔15/9
          ⇒ 3/0/4/5/9
Answer = 30459

 SECOND METHOD 
This method is useful when both the numbers are near to common bases i.e powers of base 10.
Example: 492 x 404
Solution: Here we are taking common base as 400

      ⇒ 1984|⃔368 = 198768
Here common base is a multiple of '100' so we keep two digits of right hand number and transfer rest to left hand number.

or we can also write like this: 496 x common base + 368
      ⇒ 496 x 400 + 368 = 198768


With the help of these multiplication tricks, you can multiply any two, three or four digit numbers within few seconds in mind without calculator or paper-pen. You don't need to write step 1, 2, 3 etc., you need to solve it in single line. It may look lengthy but these are shortest methods to multiply numbers mentally. You need practice only. Good Luck 👍