a) Multiplying a 2-digit number with 11.
To multiply a 2-digit number with 11 follow these steps:-
Divide the number into two parts.
Add these two parts which will form the middle number of our answer.
Insert this added part between divided two numbers.
Let us take an example to explain this. Now multiply 23 with 11.
Divide 23 into two parts 2 and 3 respectively.
Add these two parts to form the middle number (2+3) = 5.
Insert this added value i.e 5 in between 2 and 3. this will give us 253.
23 x 11 = 253
Important:-What if the sum of divided numbers exceeds 10.
In this case, just take carry from the middle number and add it to the starting number. For example:- 78 x11
So here, divided numbers are 7 and 8 and the middle part will be 7+8 =15. Now take the carry 1 and add it to 7 resulting in answer 858.
b) Multiplying a number with 11
Now, let us take our multiplication of 11 to next level. What is there is the multi-digit number how will you solve it? Its pretty simple it applies the extended rule of a)
Divide the numbers into parts such that each part is a single-digit
Now, let us start placing numbers from the back lets place the last digit of the number at back then moving forward keep placing a sum of two consecutive digits from the back.
At last, add the most significant digit to the front of the answer.
Let us understand it by taking the example 123 x 11.
now split the digits as 1, 2, 3.
take the sum of consecutive digits in order 1+2 =3 and 2+3 =5.
now place the first and last digit of the number and in-between place the sum of digits in order i.e 1 3 5 3. this gives us the 1353 answer.
123 x 11 = 1353
When the sum of digits exceeds 10 then apply the method given in section (a).
Now you can easily find product of any number with 11 without using a calculator.
c) Multiplying two 2-digit numbers.
When you will know this awesome trick, then you will be able to perform the multiplication of two 2-digit numbers easily without using a calculator. let's understand how to perform this by taking the example 31 x 12.
Multiply the ones digit vertically
Multiplying in a cross pattern and adding the results.
Multiplying the tens digit vertically.
This is how one can calculate the product of two 2-digit numbers easily.
d) Multiply two numbers close to a multiple of 10 i.e 98, 102, 998 etc.
Let us understand it by taking two examples.
Multiply 99 × 97
Multiply 103 × 105
Find by how much the number is more or less than the power of 100 and write it on the right side of the vertical line.
Either cross subtract or cross add. This will form the first part of the final answer.
Multiply the right side of the vertical line and this shall form the right side of the result.
03 15
resulting in answers 9603 10815