Multiplication by 3 Digit Numbers – Vedic Math Tricks
October 8, 2022
Simple Interest
October 20, 2022The multiplication by 2 digit number technique explained in this section is inspired from Vedic Maths. This trick will help you multiply any two digit number in your head. This is a generalized approach, you can actually get the solution even before you know it. That is, by applying the multiplication by 2 digit number technique explained in this post, you can calculate the result from left to right.
This technique is contrasting to what we have learnt in our childhood. In that, you have to multiply two digit number from right to left, which involves remembering or noting down the carry. This is a significant overhead in mental math approach. The multiplication by 2 digit number using the left to right approach, you can calculate the product in your head without worrying about the carry.
By the end of this post you will learn the following tricks
- 2 digit by 1 digit multiplication
- Multiplication 2 digits by 2 digits
In the next lesson on three digit multiplication, we have extended the two digit multiplication trick from this lesson and have used it multiply a 3 digit by a 2 digit number.
Multiplication by 2 digit numbers - Video
The approach involved in multiplication by 3 digit numbers is explained in the videos below with the help of two examples. The first example focuses on multiplying three digit numbers without using carry, while the second number deals with carry.
Multiplication by two digit numbers - Approach
As explained in the video above, we are going to use the vertical and cross wise technique of Vedic maths to multiply two digit numbers. This technique helps us easily multiply 2 digit numbers mentally. We will look into this multiplication trick by categorizing the approach to multiplication by 2 digit numbers into following sections:
- How to multiply two 2 digit numbers
- How to multiply double digit numbers by single digit numbers
Multiplication 2 digits by 2 digits
Lets learn the left to right approach to multiplication by 2 digit number. Please not that two digit multiplication technique explained here can also be calculated from right to left. But we recommend doing it from left to right, as the idea behind learning these tricks is to help enhance our mental calculation skills. Above all, mental calculation is all about calculating from left to right.
So now, given below is the two digit multiplication approach explained with the help of two examples. The approach illustrated in these examples can be used to multiply any two digit number.
Example 1: Multiply 21 and 32
- In order to carry out the multiplication by 2 digits we will divide the solution into 3 parts. The number of parts here is obtained by 2x$n$-1, where $n$ represents the value in n-digit multiplication. In case of 2 digit multiplication n is 2. Hence,
21
x 32
------------------------
? | ? | ?
- Left most part is obtained by multiplying the left most digits 2 in 21 and 3 in 32 => 2x3 = 6
21
x 32
------------------------
6 | ? | ?
- The middle part is obtained by cross multiplying between the first two digits 2 and 2 & 1 and 3, then adding the respective products => 2x2 + 1x3 = 7
21
x 32
------------------------
6 | 7 | ?
- Right most part is obtained by multiplying the right most digits in both the numbers => 1x2 = 2
21
x 32
------------------------
6 | 7 | 2
- Thus we have the result of multiplication of two digit numbers 21 and 32 is 672.
Example 2: Product of 76 and 53
- Similar to the previous example, Lets calculate the product of 76 and 53 by first dividing the solution into three parts.
76
x 53
------------------------
? | ? | ?
- Left most part is obtained by multiplying the tens digits 7 in 76 and 5 in 53=>7x5=35
76
x 53
------------------------
35 | ? | ?
- Middle part is obtained by cross multiplying between 7 and 3, 6 and 5, and adding the respective values => 7x3+6x5=21+30=51
76
x 53
------------------------
35 | 51 | ?
Note: Except for the left most part, all the other parts must contain only one digit, the excess digit if any will be carried over to the left. Hence , the excess 1 in 51 will be carried over to the left part. Thus:
76
x 53
------------------------
35 | 51 | ?
=> 40 | 1 | ?
- Right most part is obtained by multiplying the right most digits in both the numbers => 6x3 = 18
76
x 53
------------------------
40 | 1 | 18
=> 40 | 2 | 8
- Thus we have calculated the result of multiplication of two digit numbers 76 and 53 without using a calculator.
How to multiply double digit numbers by single digit numbers
Now lets learn the left to right approach to multiplication of 2 digit number by 1 digit number.
If AB is a 2 digit number that is to be multiplied with single digit number say C. Then, the left to right approach to 2 digit by 1 digit multiplication, is carried out by multiplying A with C and then B with C.
A B
x C
————
=====>
During this multiplication process, if the product of B and C results in more than 1 digit the excess digit will be carried over to the left.
Example: Product of 46 and 7
In 46 x 7, first multiply the left most digit 4 in 46 with 7 => 4x7 = 28
4 6
x 7
--------------
28 | ?
Now, multiply the units digit 6 with 7: 6x7 = 42, and then carry the excess 4 to the left. Thus 28 becomes 32. Hence we have 46 x 7 = 322
4 6
x 7
--------------
28 | 42
=> 32 | 2
What Next?
This trick requires a considerable amount of practice. But once mastered, you would be amazed with how good a mental workout it would turn out to be. For practise, you can start with 2 digit by 1 digit multiplication from left to right which will help you practise calculating carry mentally and then start with 2 digit by 2 digit multiplication.
Remember, you won't be able to master left to right multiplication over night but by putting in a considerable amount of effort you will definitely fall in love with this technique. Now take the quiz below and the exercises associated with this lesson to get started.
