In this tutorial, we are going see an interesting class of numbers like 101, 203, 10001, 201 etc. Notice an important thing here. You have 2 different numbers (may be same or different) at the end and you have 1 or more zeros in between.
What is so special, you might think. It turns out, that when you multiply any number (multiplicand) with numbers like 101, 1001, you just repeat the multiplicand twice.
Let us understand the shortcut with a very simple example: Let’s say we need to multiply 23 x 101.
When you multiply any 2-digit number with 101, you just repeat 23 twice.
Similarly, 39 x 101 would be :
Very easy right 🙂
On the similar lines, can you mentally calculate?
- 12 x 101
- 13 x 101
- 89 x 101
- 99 x 101
Multiplication of a 3-digit number with 101
Suppose, we have to multiply a 3-digit number with 101, the steps are slightly different from the previous case. Let us consider an example so that it is clear.
Let’s say we want to multiply 243 x 101
Step 1 : The first 2 –digits 24 will become the first part of the answer.
Step 2 : The last 2 –digits 43 will become the last part of the answer.
Step 3 : The middle digit in the answer is obtained by adding the first and the last digit of the multiplicand.
So, the only difference is instead of repeating the whole digit, you repeat the first 2 and the last 2 digits.
Can you multiply 856 x 101 ?
Notice the carry-over in the addition. We can retain only 1-digit in the addition.
It does not always have to be 101. The steps remain same even if the number is say 203, 304. However, in this case, the answer will be scaled according to the multiplicand.
Let’s say we need to multiply 43 x 205. The steps are illustrated in the figure.
Instead of 101, we have 205 here. So, you scale the first part of the answer by 2 and last part by 5.
Step 1 : The multiplicand 43 is doubled to get 86 to get the first part of the answer.
Step 2 : The multiplicand 43 is multiplied by 5 to get 215. However, we can retain only 2-digits. So, 2 is carry-forward to get the final answer as 8815.
Similarly, can you try 74 x 603 ?
Multiplication by 1001
If the multiplier is 1001, you just repeat the 3-digits of the multiplicand twice. Let’s say we want to multiply 359 x 1001.
So, 359 x 101 = 359359
Similarly, 453 x 1001 = 453453
Now consider the multiplication, 435 x 3002
Step 1 : The multiplicand 435 is multiplied by 3 to get 1305 which becomes the first part of the answer.
Step 2 : The multiplicand 435 is multiplied by 2 to get 870 which forms the RHS part of the answer.
Now, what if the multiplicand is a 2-digit number. Notice the multiplication 43 x 3002.
A zero is added in the beginning so that the number of digits in multiplicand is 1 less than the multiplier. The rest of the steps remains same.
On the similar lines, can you multiply :
- 23 x 1001
- 848 x 1001
- 72 x 2004
- 834 x 2002
- Even if one of number is bigger say 10001, 1000001, the multiplicand is repeated twice to get the final answer.
- Similarly if you multiply the number 24 by 10101, you notice that the multiplicand is repeated thrice and 4 times if the multiplicand is 1010101 and so on.
I hope you find this tutorial useful. Please leave a comment if certain point in the tutorial is not clear.