# Multiplying 2 numbers which are reverse

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/ a2+b2/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 a2+b2.

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/a2+b2+c2/ab+bc/ac.

or

ac/ b(a+c)/a2+b2+c2/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 a2+b2+c2.

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.

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

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