Two digit multiplication in 2 seconds

Ex : 33 x 37

This is very easy. Matter of seconds to complete the multiplication

33 x 37 = 3 x 4 / 7 x 3
             = 12 / 21
             = 1221

Please remember this is special case

You can apply this method if it satisfies two conditions

1. ten's digit should be same

2. sum of 1's digits should be 10

In 33 x 37

10's digit is 3 in both number
sum of 1's digit = 3 + 7 = 10

Let  us try one more example

42 x 48 = 20 / 16 = 2016

What exactly you are doing is

1's digit number in the result = product of 1's digit = 2 x 8 = 16

10's digit number in the result = 10's digit number x (10's digit number  + 1)

                                               = 4 x ( 4 + 1) = 4 x 5 = 20

No carry forward. Just you are taking numbers as it is
i.e result = 2016

Try following examples  and check the result

Ex 1.   51 x 59 = ?
           23 x 27 = ?
           94 x 96 = ?
           76 x 74 = ?


          

Today let me try with base 30.

Ex : 34 x 37

step 1: base is 30
step 2: 34 x 37
     +4    + 7

step 3: 34 + 7 / 4 x 7
          = 41 / 28
          = 41 x 3 /  28 ( multiply with 3 as base is 30 )
          = 123 + 2 / 8  ( carry forward 2 )
          = 125/8  
          = 1258
  
Actually these many steps not required. For your understanding purpose, I am explaining step by step.

 One more example

Ex 2 : 33 x 37

base = 30
result = 33 + 7 /  7 x 3
          = 40 / 21
          = 40 x 3 / 21    ( multiply with 3 as base is 30 )
          = 120 / 21        ( carry forward 2 )
          = 1221


we can do second example in  very simple way. How?

Wait till next post...

Did you find answer for 16 x 14 ?


Base for 16 x 14 is 10
               +6   +4

Unit's place digit = 6x4 = 24
10's place digit  = 16+4 = 20o

result = 20 / 24  = 20+2 / 4  ( 2 carry forward )
          = 224

Base method is very useful in squaring number.

Now what is the result of 23 x 22 ?


Here what is the base? 20

23 x 22
 +3    +2

unit's place digit = 3x2 = 6
10s place digit = 23 + 2 = 25
result = 25 / 2 = 252

Is that correct? No

Please note in this examples 20 is the base. So you have to multiply 10's digit with 2

Correct method :
10's place digit = 23 + 2 = 25 x 2  ( As 20 is base, multiply with 2 )

result = 50 / 6 = 506

Now you tell me if the base is 30, multiply with ?

if the base is 30, multiply 10's digt  with 3

if the base is 40, multiply 10's digt with 4

Two digit multiplication - special case

I would like to introduce special case in multiplication. This is base method multiplication.

What is base method multiplication?

Let me explain by taking one example.

Ex : 15 x 17

15 = 10 + 5
17 = 10 + 7

So here 10 is base

15 x 17
 +5   +7

 unit digit = 5 x 7 = 35
10's digit = 15 + 7 = 22

So result = 22 / 35
Please note in units place two digits are there. As I mentioned in earlier posts 3 should be carried.

So result = 22+3 / 5 = 25 / 5 = 255

So now you try for  16 x 14 = ?.

Bottom line is express both number into base of some number. Here that is 10

15 = 10 + 5 and 17 = 10 + 7

Unit place number is multiplication of  numbers of above the base i.e. 5 x 7 = 35

10's place number is 15 + 7 or 17 + 5 = 22

If you understand this method, multiplication matter of seconds. Try and expertise this. Next methods depends on this method.

Two digit multiplication

I am back...

Lets look at two digit multiplication in generic way

Ex : 23 x 45

Here two numbers are there
first number :  23
first digit  : 3 second digit : 2

second number : 45
first digit  : 5 second digit :4

Result :

first digit = first digit x first digit = 3 x 5 = 15
second digit = first digit x second digit  + second digit x first digit
                    = 3 x 4 + 2 x 5 = 12 + 10 = 22
third digit = second digit x second digit = 2 x 4 = 8

wherever two digits are there in result, carry one digit to next place.

first digit in result = 15 = 5 and 1 carry forward to next place
second digit in result = 22 + 1 ( carry forward )
                                 = 23 = 3 and 2 carry forward to next place
third digit in result = 8 + 2 ( carry forward )
                              = 10 = 0 and 1 carry forward to next place

So the result is 1035


result = second digit x second digit / first digit x second digit + second digit x first digit / first digit x first digit


In simple terms

ab x  cd = ac / ad + bc / db

b and d are first digits of numbers ab and cd
a and c are second digits of numbers ab and cd