Friends, if you want to multiply any number made of digit 9 with any digit between 1 to 9; you can do it in seconds. How? Just see.
For example, take 99 which is to be multiplied by 2,3,4,5,6,7,8 and 9.
99×2= 198;. 99x 3= 297
99×4=396:;. 99×5 = 495
99x 6=594:;. 99 x7=693
99x 8=792;. 99x 9=891
You can see some similarities in above multiplications. What it that. Let me explain you.
1) You might have observed that in all above examples, digit 9 is in between two digits.
2) The first and last digits are nothing but multiplication of 9 and the number given for multiplication i.e.2,3,4,5,6,7,8 & 9.
So simple rule can be established here:
1) To multiply any number made of 9 with any digit from 1 to 9, just multiply 9 with given number.
2) Write down the answer keeping distance between the digits.
3) Now simply insert 9 in between these two digits.
That is the answer.
You can check it by considering 999, 9999 and any more.
We can also form another rule for this:
1) Just multiply 9 and the digit given for multiplication, i.e. 2,3,4……….
2) Write down the answer i.e. 9×2= 18, keeping some space in between 1 and 8.
3) Now add 1 with 8 and write down the answer i.e. 9 in between 1 and 8.
4) The answer is 198.
You can choose any one out of these two methods.
It’s simple to multiply any number with 99 or 999 or 9999,etc. by any number.
If you want to multiply 999 with 756, just add 1 to 999. It will become 1000. Multiply it by 756. You will get 756000. Write it down. Now sustract 756 from 756000. You will get answer as 755244.
Take another example.
You want to multiply 99 with 75. Add 1 to 99 and multiply with 75. Will get 7500. Subtract 75 from 7500. Will get 7425.
Friends, multiplication by 22 to any number made of 2 is very very easy.
Suppose I want to multiply 22 by 22. Just write 44 with some space between two digit. Now count the number of digits in the figure to be multiplied by 22. It is two. Now write 8 in between 44. You got the result as 484.
2nd example. Start multiplication of 22 with 2222. The answer you get is 48884.
You can see various examples in this video which is created by me.
friends I am giving here a simple formula created by me for multiplication of any number made of digit 9 with any other number.
for example take 99 on first instant. I am asked to multiply it by 8. Its very simple and you can do it orally.
1) Multiply 9 with 8. We will get the answer as 72.
2) Now write 72 keeping some space in between.
3) Now add 7 and 2 we will get 9.
4) Write 9 for one time in between 7 and 2, since there are 2 digits in given number.
5) the answer will be 792.
You might have understood the formula.
Now take another example. Consider a Number 99999 to be multiplied by 9.
Step 1 ) 9×9= 81
2) 8 1
3) 8+1=9 write 9 in between 8 and 1 for 4 times since there are 5 digits in given number.
You answer will be 899991
I would like to introduce you a simple formula for getting square of any number ending 5.
(x5)2= x*(x+1)25 This is the formula.
Here x is the digit prefix to 5 of the given number. On right hand side x*(x+1) is only prefix to 25.
Suppose 25 is the given number. Hence x=2
to get square of 25 write 25 on right hand side.
Now multiply 2 by (2+1) i.e. 3, we got 6. Write this 6 as prefix to 25. Here is the answer 625.
Now consider 105 as a given number which is to be squared.
First write 25 on right hand side. Now multiply 10 by 11. We got 110. Write 110 at the left side of 25 the number is 11025. This is the square of given number 105.
We can try with another number. Take 175.
As explained earlier write 25 at right side. Now multiply 17 by 18 answer is 306, write it as prefix of 25, the answer is 30625.
Cross check is with the help of calculator.
Today we will see how to get square of any number made of digit 6. Let us assume one number 6666. To get square of this number we have to execute following steps.
1) Write down square of 6 i.e. 36 keeping some gap in between both the digits.
2) Count how many 6 are there in the given number. Here there are 4 digits.
3) Subtract 1 from 6 and we got 5 which we have to write down to the left of 6 for 3 times i.e. 1 less than above 4.
4) Now add 1 to 3 and we got 4 which we are supposed to write down to the left of 3 for 3 times similar to 5 which we had already written.
5) The result we got is like this
44435556 which is the square of 6666.
It is very easy to multipky any two digit number by 11. Let me explain you how.
Suppose you want to multiply 36 by 11
1) Write 36 keeping some gap between both the digits.
2) Now add both these digits. You will get 3+6=9
3) Write this result of addition in between 3 and 6. You got a number 396.
This is the multiplication of 36 and 11 i.e. 396
You can cross check it with calculator.
Take another number 76
As explained above write 76 keeping some gap between both the digits.
After adding 7 & 6 we get 13
Since the result is a two digit number we must first write 3 between 7 and 6
And the carry over 1 shall be added to first digit of the given number i.e. 7. By addition we got 8.
Now replace pre-written number 7 by 8. Finally we got one number i.e. 836
This is the multiplication of 76 and 11.
Now try it yourself with other numbers.
We had seen how to get square of any number made by digit 1 easily. Now I would like to show your my simple formula for getting square of any number made by digit 3.
Step 1: Take any number made by digit 3. suppose the number is 333.
Step 2: First write the square of 3 i.e 9.
Step 3: Now by reducing this number 9 by 1 you will get 8. Now count the number of digits in the given number 333. You can see that there are 3 digits in the number. Reduce this 3 by 1. You will get 2. Write 8 for two times to the left of 9.
Step 4: Now simply write zero to the left of last 8 from the right side.
Step 5: Now as we had written 8 for two times write 1 for two times to the left of zero.
Step 6: You got a number as 110889. This is the square of given number 333.
Similarly square of 33333 can be calculated in a fraction of second. It will be 1111088889. Its very simple formula. Try it and give your valuable comments.