Multiplication trick

Vedicmath trick to multiply any two 3 digit numbers can be done mentally in seconds. Three digit multiplication is not a difficult task as much as we all dread.In fact, you will enjoy doing 3 digit multiplication once you know this amazing trick. Take your time to understand the technique and practice a lot until you master the technique.Because it so happens that we read a lot of tricks and techniques but can’t remember the exact technique during exam and feel so helpless.You don’t want to be that person!

Let us understand the technique using an example

Suppose we want to multiply 121 by 310.Step 1:First multiply the unit digits of both the numbers.
We get 0 x 1= 0 as shown below

Step 2:Now multiply unit digit of second number(310) with tenth digit of 1st number(121) and also multiply unit digit of first number(121) with tenth digit of 2nd number(310) and add the resulting products.
We get,(0 x 2) + (1 x 1)=1

Step 3: Now multiply unit place digit of the second number(310) with the hundredth place digit of 1st number(121)
And multiply unit place digit of first number(121) with hundredth place digit of second number(310)
Also multiply tenth place digit of second number(310) with tenth place digit of first number(121)
And find the sum of the resulting products.
We get (0 x 1) + (3 x 1) + (1 x 2) = 5

Step 4:Multiply the tenth place digit of second number(310) with the hundredth place digit of 1st number(121) and multiply the tenth place digit of 1st number(121) with hundredth place digit of 2nd number(310) and find the sum of the resulting products.
We get (1 x 1) + (3 x 1) = 7

Step 5:Multiply the hundredth place of second number(310) with the hundredth place digit of first number(121).
We get (3 x 1) = 3

We have arrived at our final answer!

121 x 310 = 37510

Shortcut to square any number from 90 to 99 is one of my favorite that I like to apply when I see a number such as 98 or 99 as all I need to know is how to subtract and square of numbers from 1 to 9.

Now lets go through the steps

Step 1:Assume 100 as base and find the difference between the number to be squared and 100.

Step 2:Subtract the difference in step 1 from the number to be squared to find tenth place digit.

Step 3:Square the difference and place it next to step 2.

Once you know the technique you can square any number from 90 to 99 mentally.

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Example 1: 98²=?
Step 1:Assuming 100 as base, we shall find the difference
100-98=2
We get the difference as 2

Step 2:Subtracting the difference(2) from the number to be squared(98) we get,
98-2=96
96 is the tenth place digit

Step 3:Squaring the difference we found in step 1 we get
2²=4
4 is the Unit place digit.
Ans 98²=9604

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Example 2: 99²=?

Step 1:Assuming 100 as base, we shall find the difference between the number to be squared(99) and 100.
100-99=1
We get the difference as 1

Step 2:Subtracting the difference(2) from the number to be squared(98) we get,
99-1=98
98 is the tenth place digit

Step 3:Squaring the difference we found in step 1 we get
1²=1
1 is the Unit place digit.

Ans   99²=9801

Example 3: 97²=?

Step 1:Assuming 100 as base, we shall find the difference between the number to be squared(97) and 100.
100-97=3
We get the difference as 3

Step 2:Subtracting the difference(3) from the number to be squared(97) we get,
97-3=94
94 is the tenth place digit

Step 3:Squaring the difference we found in step 1 we get
3²=9
9 is the Unit place digit.

Ans   97²=9409

You must be wondering we have learnt so many multiplication tricks for 2 digit numbers,so how is this going to be helpful.Well, Knowing new tricks and where the trick can be applied to get the answer quickly can make all the difference. 2 digit multiplication trick whose tens digit is same is one of those tricks that you will learn today.

Condition to apply this trick is 
When the ten’s place digit is same and the unit’s place digits add up to 10 then you can apply a shortcut trick to easily multiply any 2 digit numbers.

Step 1:To get the unit’s place digit multiply the unit’s place digit of the both the numbers.

Step 2:To get the ten’s place digit multiply the ten’s place digit with its consecutive(next) number.

Step 3:Place the result obtained in step 2 to the left of the result obtained in step 1.

Let us now practice some examples

Example 1: 26 x 24=?
We observe that ten’s place digit of both numbers=2
and by adding unit’s place digit of both numbers(6+4=10)we get 10.

Hence, we can apply this trick

Step 1:Multiplying the unit’s place digits we get
Unit’s place digit=6 x 4=24

Step 2:Multiplying ten’s place digit by its consecutive number we get
Ten’s place digit=2 x 3=6

Step 3:Placing the result of step 2 to the left of the result obtained in step 1 we get
624

Ans  26 x 24=624

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Example 2: 43 x 47=?
We observe that ten’s place digit of both numbers=4
and by adding unit’s place digit of both numbers(3+7=10)we get 10

Step 1:Multiplying the unit’s place digits we get
Unit’s place digit=3 x 7=21

Step 2: Multiplying ten’s place digit by its consecutive number we get
Ten’s place digit=4 x 5=20

Step 3:Placing the result of step 2 to the left of the result obtained in step 1 we get
2021

Ans  43 x 47=2021

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Example 4: 65 x 65=?
We observe that ten’s place digit of both numbers=6
and by adding unit’s place digit of both numbers(5+5=10)we get 10

Step 1:Multiplying the unit’s place digits we get
Unit’s place digit=5 x 5=25

Step 2: Multiplying ten’s place digit by its consecutive number we get
Ten’s place digit=6 x 7=42

Step 3:Placing the result of step 2 to the left of the result obtained in step 1 we get
4225

Ans  65 x 65=4225

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Example 5: 71 x 79=?
We observe that ten’s place digit of both numbers=7
and by adding unit’s place digit of both numbers(1+9=10)we get 10

Step 1:Multiplying the unit’s place digits we get
Unit’s place digit=1 x 9=09

Step 2: Multiplying ten’s place digit by its consecutive number we get
Ten’s place digit=7 x 8=56

Step 3:Placing the result of step 2 to the left of the result obtained in step 1 we get
5609

Ans  71 x 79=5609