Multiply any 3 digit numbers

 

In the previous tutorial on multiplication of any 2-digit number, we learnt how to multiply any 2-digit numbers  using criss-cross method of multiplication.

In this tutorial,  we will understand a very important mathematical shortcut of multiplying any two 3 digit numbers using the criss-cross multiplication technique.

For students preparing for competitive examination, You might come across, many multiplications in the competitive examinations where you might be asked to multiply two 3-digit number.

If you know criss-cross method, you can save a lot of time by eliminating the choices at the end of each step of criss-cross multiplication.
The number of steps in a 3 x 3 multiplication is 5. Let’s understand the steps with an example.

 

Example : Suppose you want to multiply 132 x 214.

Step 1 :   Write the numbers one below the other. Multiply the digits in the unit place as in 2×2 multiplication, that is 2×4=2. This will be the unit digit of the answer as well.

criss-cross_31


Step 2 :
 Now, cross multiply the digits in the 10’s and unit’s place to get the digit in the 10’s place of the answer.

criss-cross_32


Step 3 :
 Now, notice the criss-cross multiplication.  Here, we multiply the terms (1×4), (2×2) and (3×1) and then add these terms to get 11.


criss-cross_33


Step 4 :
 Now, repeat Step 2 with the digits in the 100’s and the 10’s place.

criss-cross_34


Step 5 :
 This is the last step in the multiplication. Now, repeat Step 1 with the digits in 100’s place.

criss-cross_35_1

 
The complete steps involved in the calculation is illustrated in the figure :

 

criss-cross_36

 

Notice the carry-forward in each step.

On the similar lines, can you multiply,

  • 423 x 234
  • 124 x 465
  • 567 x 890
  • 646 x 772

Easy :) ?

I hope this tutorial is useful. If you have any doubts concerning this tutorial, please leave a comment, I would be glad to help.

Kiran Chandrashekhar

Hey, Thanks for dropping by. My name is Kiran Chandrashekhar. I am a full-time software freelancer. I love Maths and Mathematical Shortcuts. Numbers fascinate me. I will be posting articles on Mathematical Shortcuts, Software Tips, Programming Tips in this website. I love teaching students preparing for various competitive examinations. Read my complete story.

10 Comments

    • Thanks so much Santanu for pointing it out. I have corrected it 🙂
      Kiran

  1. Great tutorial…very helpfull : )
    There is a miscalculation in step III, the result should be 11 instead of 14

    • Thank you so much for pointing it out. I am extremely sorry for the inadvertent error though.
      I am glad you liked it.

      Thanks
      Kiran

  2. sir pls solve that multiply numbers 68*73

    ur steps are:
    1st step:
    8*3=27
    2nd Step:
    (6*3)+(7*8)
    18+56=74
    3rd Step:
    6*7= 42

    therefore, 42/74/27

    and written off 42/4/7
    7 2
    then 4987 this anwer is wrong sir .
    pls give me detailed soultion ur reply im waited

    • Hello Ramya,

      Here are the steps :

      68*73 = 6*7 / (6*3 + 8*7) / 8*3
      = 42/74/24
      =4964

  3. the vth step should be 2 and not 8.
    anyway thanks for such an eloquent explanation.

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