You might have already went through my tutorial on multiplying any 2, 3 or 4-digit number using a technique called Criss-Cross method of multiplication. If you not practiced the technique, I would advice you understand the shortcut before going through this tutorial.

You can refer my articles on Criss – Cross method of multiplication here :

In this article on Mathematical Shortcuts, we are going to learn about multiplication between special group of numbers. You often come across questions in the competitive examinations, where you are asked to multiply 2 numbers where one number is exact opposite to the other number.

For example, numbers like 13 x 31, 25 x 52, 123 x 321 etc.

Let us consider a general 2-digit number *ab *and see how does the product *ab *x* **ba *look like :

So, when you multiply any 2-digit numbers, which are in reverse, the product would be in the form: *ab/ a ^{2}+b^{2}/ab. *

So, the product will have 3 terms( 3 more digits). Notice the first and the last term is same *ab* and the middle term is *a ^{2}+b^{2.}*

Consider an example, 24 x 42. With this shortcut, you can easily write the product as 8/20/8.

So, 24 x 42 =1008

Similarly, 67×76 = 42/85/42

So, 67×76 =5092

Very easy right ðŸ™‚

**Exercise:** Try to obtain the product of the following numbers:

- 18 x 81
- 92 x 29
- 49 x 94
- 86 x 68

Let us now consider a general 3-digit number *abc* and see how does the product *abc* x *cba* look like :

So, when you multiply any 3-digit numbers, which are in reverse, the product would be in the form:

*ac/ ab+bc/a ^{2}+b^{2}+c^{2}/ab+bc/ac. *

or

*ac/ b(a+c)/a ^{2}+b^{2}+c^{2}/b(a+c)/ac.*

So, the product will have 5 terms. Notice the first and the last term is same *ac* followed by *b(a+c)* and the middle term is *a ^{2}+b^{2}+c^{2}.*

Notice the similarity in the terms in 2-digit and 3-digit multiplication.

Consider an example, 235 x 532.

With this shortcut, you can easily write the product as 10/21/38/21/10

So, 235×532 =125020

Similarly, 617×716 = 42/13/86/13/42

So, 617×716 =441772

So, just write down some random number and take its reverse and see if you get the right answer everytime.

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**Exercise:** Try to obtain the product of the following numbers:

- 612 x 216
- 178 x 871
- 908 x 809
- 767 x 767

I would leave the 4×4 multiplication of two numbers which are reverse to you. If you have any doubts, please leave a comment in the comments section or write to me an email, I would be glad to help you.