Multiplying 2 numbers with the same unit digit

 

This is an interesting find. Suppose, you have to multiply 2 numbers having the same unit digit, how do you fast multiply such numbers mentally.

In this tutorial on mathematical shortcut, we will learn, how to multiply 2 numbers who’s unit digit remains same. The rest of the digit can be any anything.

For example, this shortcut can be used to multiply the numbers such as 72 x 82, 53 x 33, 181 x 281  etc.

Let’s say, we want to multiply 72 x 82. This satisfies the condition, as the unit digit is same.

The steps are illustrated in the following figure.

 

multiply_same_1s_2

 

Step 1:  Break the number such that unit digits is on the right and the rest of the digit ( i.e., 7 in this case) is on the left.

multiply_same_1s_1

Step 2 :  Square the unit digits (22).

Step 3 :  Add the 10’s digits (7+8=15) and multiply the sum with the unit’s digit (2).

Step 4 :  Multiply the 10’s digit. Notice the carry in each case. Notice only 1-digit is retained in each stage and the rest of the digits is carry-forward.

So, 72 x 82 = 5904

 

Similarly, can you compute what is 124 x 154 ?

 

multiply_same_1s_3

 

Let’s consider another example : 124 x 324. Notice the difference between this and the previous example. In the previous example, only the unit digit was same and rest of the digits was different.

 

multiply_same_1s_4

 

Step 1 : Break the numbers, such that number 24  are on one side, and the rest of the digits (1 & 31) are on the other side.

Step 2 : Square the number 24. We get 576. Earlier, we would keep just a single digit and carry-forward the rest of the digits. In this case, we are multiplying 2-digits at a time. So keep 2-digits 76 and 5 is carry forward.

Step 3 : Add the digits (1 + 3 = 4) and multiply the sum with the digit 24 to get 96. Add 5, the carry from previous Step 2 to get 101.  Again here, we will retain both the digits. 1 is carry forward.

Step 4 : In the last step, multiply the digits 1 and 3.

It is important to know, why we are taking 2 digits at a time whereas in the previous example, we are retaining a single digit and the rest of the digits are carry-forward.

In this example, both the digits in the units and the 10’s place are same and the rest of the digits are different.

 

Note If you find the multiplication of 3-digit numbers confusing, just try to remember the technique used in 2-digits. It requires lot of practice to master this shortcut when the numbers are 3 or more digits.

 

Exercise : Can you multiply ?

  • 71  x 81
  • 124 x 234
  • 56 x 86
  • 314 x 214

Please contact me if some point in the tutorial is not clear. 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.

One Comment

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