How to multiply 432 with 354 quickly using vedic math trick?



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I already wrote an article about multiplying two 4-digit numbers in a short time. Here we are having two 3-digit numbers instead of 4 but the method to solve it is still the same. Let us proceed.

Example 1:

First, let us write the two numbers in the vertical order as below so that it makes a square with 2 rows and 3 columns.

4 3 2
3 5 4

Step 1: Select the first column with two vertical digits 4 and 3. We will multiply these two digits as below.

4 * 3 = 12 (consider this as note 1 value)

Step 2: Now select the first two columns containing 4 digits > 4, 3, 3 and 5. We will cross-multiply and add together as below.

4 * 5 + 3 * 3 = 29 but we will write only 9 and carry the first digit that is 2.

So, 9 (consider this as note 2 value and carry of 2 from above)

Step 3: Now select all three columns containing 6 digits 4, 3, 2, 3, 5 and 4. We will cross-multiply 1st and 3rd columns and will also multiply the two digits in the 2nd column and add them all as below.

4 * 4 + 2 * 3 + 3 * 5 = 37 (but we will write only 7 and carry the first digit that is 3).

So, 7 (consider this as note 3 value and carry of 3 from above)

Step 4: Now select the last two columns (not the first two columns) containing four digits 3, 2, 5 and 4. We will cross-multiply the two columns and add as below.

3 * 4 + 2 * 5 = 22 (but we will write only 2 (2nd digit) and carry the first digit that is also 2).

So, 2 (consider this as note 4 value and carry of 2 from above).

Step 5: Now we will select the last column containing two digits 2 and 4. We will multiply the two and add them as below.

2 * 4 = 8 (consider this as note 5 value. There is no carry in it).

To get the final answer we will group the values of note 1 to note 5 in below order but before that, we need to add the carry.

note 1 - note 2 - note 3 - note 4 - note 5

12 (note 1 value) +2 (carry of note 2) = 14

9 (note 2 value) + 3 (carry of note 3) = 12

7 (note 3 value) + 2 (carry of note 4) = 9

2 (note 4 value) + 0 (there is no carry so zero) = 2

8 (note 5 value) = 8

arranging the new notes (after adding the carry) as below will give the answer.

note 1 (14) - note 2 (12)- note 3 (9) - note 4 (2) - note 5 (8)

but this is still not the final answer

This is because anything greater than or equal to 10 from note 2 to note 5 (the end note) is not written as it is. The value of note 1 can, however, be greater than or equal to 10.

We see the value 12 in note 2 which is greater than 10. We will write 2 and carry 1 to be added to the note 1 and then the results will be as below:

note 1 (15) - note 2 (2)- note 3 (9) - note 4 (2) - note 5 (8)

writing or grouping the values of notes (in brackets) in the same sequence as above we get.

152928 (this is the final answer of 432 * 354).

With so many steps to follow this may look complicated initially but once you are used to it, you can multiple in less than 1 min which will not be possible if you do the usual way of long multiplication.

But there is also one more easier way to multiply two 3-digit numbers

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Written by: Rajesh Bihani ( Find me on Google+ )

Disclaimer: The suggestions in the article(wherever applicable) are for informational purposes only. They are not intended as medical or any other type of advice