multiply tricks
Easy multiplication technique:
When the last digits of each of the two numbers sums up to 10, and the first digits of both the numbers is the same, you can multiply the same mentally using this easy trick.
If there is a multiplication problem involving two 2 digit numbers, both of which have the same first digit while the last digits sum up to 10 , for example 28 and 22, here both the numbers have the same first digit 2 and the last digits (8 and 2) sum up to 10.
Here’s how to solve it;
First you add 1 to the common first digit and multiply the answer with that digit.
Eg.
2 is the common digit in this example, hence we shall add 1 to it,
2+1= 3
Now multiply this with the common digit, i.e. 2
Hence 2*3 =6
This answer will form the first digit of the final answer.
Now multiply the right hand side digits, i.e. 2 and 8
2*8 = 16.
This answer forms the last two digits of the final answer
Therefore 22*28=616
Now let us do another example to understand this better,
39*31= [3*(3+1)] [9*1]
Here the common digit is 3 hence we add 1 to it and then multiply this number obtained by the common digit,
= [3*4] [9*1]
We also multiply the right hand side digits of both the numbers,
= 1209
(In this case since the multiplication of the right hand side digits results in a single digit number we write it as 09 hence the answer is 1209)
Let us try another example,
Let us say we need to multiply 73*77
In this case the common number is seven and the right hand side digits sum up to 10 as well. So as usual we shall add 1 to the common digit and then multiply the answer with the common digit and then multiply the right hand side digits as well to get the final answer.
73*77= [7*(7+1)] [7*3]
= [7*8] [7*3]
= 5621
Do you want to crosscheck with a calculator and see if it is right please…??
Are you believing in these tips yet or should we solve another small example to seal the belief?
Let us try another one shall we?
How about trying to multiply 42*48
Since the common digit in this case is 4 we shall add 1 to 4
4+1= 5
Now multiply this by the common digit
Hence, 5*4=20
Now we shall multiply the right hand side digits to get the last two digits of the answer,
2*8=16
Hence 42 * 48 = 2016.
Easy multiplication of two digit numbers:
It is very easy to carry out multiplication of two 2 digit numbers without having to use a pen and paper. To multiply two 2 digit numbers we will have to assume that the answer will be a three digit number. To find the first digit of the answer multiply vertically the left hand side digits of both the numbers, the second digit of the answer is determined by cross multiplying the digits in the two numbers and adding them together. And lastly, the last digit is determined by multiplying vertically the right hand side digits of the two numbers.
To understand better let us try and multiply 45*23
First multiply vertically the left hand side digits i.e. 4*2 =8
Then cross multiply and add, [4*3] + [5*2] =12+10=22. Since the number is greater than 10 we carryover 2 and add it to the first digit i.e. 8.
Lastly we multiply the right hand side digits to get 5*3=15 again we carry 1 and add it to the previous digit. Hence the answer is 1035.
This method is very simple and fast and can be used to make mental estimations of complex multiplications.
Let us try another example,
32*24
In this case as well, we will first multiply the left hand side digits of the two numbers,
[3*2]= 6
Now we shall cross multiply and add the remaining digits,
[3*4]+[2*2]=12+4=16
Since this is greater than 10 we shall carry over the one and add it to the answer obtained in step one.
Lastly we shall multiply the right hand side digits of the two numbers
[2*4]=8
Hence the answer obtained on multiplying 32 with 24 is 768.
To multiply two three digit numbers:
We follow a method similar to the one stated above. We start by multiplying the last 2 digits of both the numbers. Then we cross multiply and add the last two digits of the numbers. Following which we cross multiply and add all the digits of the numbers. We then cross multiply and add the first two digits of the two numbers and then we multiply the left hand side digit of the numbers. Confused? Let us try and solve it using this example, 423*120
Firstly we multiply the left hand side digits of both the numbers,
3*0=0
Then we cross multiply and add the last two digits of the numbers
[2*0]+ [3*2] =6
Now we cross multiply and add all the three digits
[4*0] + [3*1] + [2*2]=0+3+4=7
Following which we cross multiply and add the first two digits from the left hand side of the numbers,
[4*2]+ [2*1] =8+2=10 (carry over one)
Then lastly we multiply the left hand side digits to get the first digit of the answer.
4*1=4 (add 1 which was carried over from the previous step)
Hence the answer is 50760.
Now let us try and multiply 561*321
Again on the same lines as the last example, we multiply the right hand side digits of both the numbers,
1*1=1
Then we cross multiply and add the last two digits from the right hand side of the numbers
[6*1]+ [2*1] =8
Then we cross multiply and add all the three digits,
[5*1]+ [3*1] + [6*2] =20 (carry over 2)
Following which we cross multiply and add the first two digits on the left hand side,
[5*2]+ [6*3] =10+18=28 (add two which was carried over)= 30(carry over 3)
And lastly we multiply the first digits on the left hand side of the numbers to get the first digit of the answer,
5*3=15 (add 3 which was carried over)
Hence the answer is 180081
Confused? Let us do another one together,
Multiply 852*110,
2*0=0
[5*0]+ [2*1] = 2
[8*0]+ [2*1] + [5*1] =2+5=7
[8*1]+ [5*1] =13 (carry one to the next step)
8*1=8 add the one carried forward = 8+1=9
Hence the answer is 93720.
Thumb rule to multiply any number by 11:
If you have to multiply any number by 11 , the first and last digits of the answer will be the digits of the answer and the middle digit will be occupied by the sum of the two digits. For example if we have to multiply 43 by 11.
43*11 = 4 [3+4] 3
The first and last digits of the answer are occupied by 4 and 3 and the middle will be the sum of the two. Hence the answer is 473.
Now let us try and multiply 72 by 11
The answer will be 7 [7+2]2= 792.
To multiply numbers with a number consisting of only nines:
If you multiply with a smaller number consisting of nine, then the number is rounded up to the nearest power of 10. Multiply the given number by that power of 10 and then subtract the original number from it.
For example 9 * 2765= [10*2765]-2765
= 27650-2765
=24885
Taking another example let us try and understand it better,
9*5643
The nearest power of 10 is 10 hence we multiply 5643 by 10 and then subtract the number from it to obtain the answer.
I.e. 9* 5643= [10*5643]-5643
=56430-5643
=50787
If the multiplication is with a larger number consisting of nines, then we will calculate the answer in two parts, the left hand side of the answer is obtained by subtracting 1 from the number in question and the right hand side of the answer is obtained by subtracting this number obtained from the number containing nines. To understand this let us consider the following example,
9999*6754
To calculate the answer for starters let us subtract 1 from 6754
6754-1=6753
This is the left hand side of the answer.
Now we shall subtract this number obtained from 9999 to get the other part of the answer.
9999-6753= 3246
Hence the answer obtained on multiplying 9999*6754= 67533246.
This method can be used to do complex calculations within seconds.
Let us try another example
99999*8765
Subtract 1 from 8765
8765-1=8764
Now subtract this number from 99999
99999-8764= 91235
Hence the answer is 876491235.
I hope these 15 easy tips have helped you in being able to calculate rapidly and solve problems without having to resort to any mechanical and physical aid.