math tricks

In the previous post we learnt how to multiply any number from 10 to 19 by 5 in seconds.Today we are going to learn another cool trick to multiply any number from 20 to 29 by 5 in seconds.

Let us see the steps 
Step 1: Assume the base as 20

Step 2: Multiply the base by 5

Step 3:Multiply the unit place digit by 5

Step 4:Add the results obtained in step 2 and step 3


Now lets consider a few examples to understand better

Example 1:21 x 5 = ?

Step 1:We assume the base as 20.

Step 2:Multiplying the base by 5 
          We get 20 x 5 = 100

Step 3:Multiplying the unit place digit by 5
          We get 1 x 5 = 5

Step 4:Adding results obtained in step 2 and step 3 
           We get 100 + 5 = 105

Ans 21 x 5 = 105


Example 2:26 x 5 = ?

Step 1:We assume the base as 20.

Step 2:Multiplying the base by 5 
          We get 20 x 5 = 100

Step 3:Multiplying the unit place digit by 5
          We get 6 x 5 = 30

Step 4:Adding results obtained in step 2 and step 3 
           We get 100 + 30 = 130

Ans 26 x 5 = 130

Another amazing way to multiply any 2 digit number by 15. I especially love to use this trick when the given number is easily divisible by 2. Shortcut to multiply 2 digit number by 15 is the easiest to mentally find answer.

Shortcut to multiply 2 digit number by 15

Step 2: Adding the given number and the result obtained in step 1
we get 56 + 28 = 84

Step 3:Placing zero next to step 2
we get 840

Ans 56 x 15 = 840

Whenever you want to multiply any 2 digit number by 5, this trick is simply amazing to use.We shall learn this trick using an example.

Suppose we want to multiply 16 by 5
Step 1:Assume the closest round number as base
           In our example,we can assume 10 as base.

Step 2:Multiply the base by 5.
            We get 10 x 5 = 50

Step 3:Now multiply unit place digit by 5
            We get 6 x 5 = 30

Step 4:Add result obtained in step 2 and step 3
            We get 50 + 30 = 80

Ans 16 x 5 = 80 


Lets see another example
Example 2:17 x 5=?
Step 1:Assuming 10 as base

Step 2:Multiplying the base by 5 
           We get 10 x 5 = 50

Step 3:Multiplying the unit place digit by 5 
          We get 7 x 5 = 35

Step 4:Adding step 2 and step 3 
           We get 50 + 35 = 85

Ans 17 x 5 = 85

Shortcut to multiply 2 digit by 111 is one of those awesome tricks that you can use to quickly multiply any 2 digit number by 111. 

Let us now go through the steps

Step 1:Write down the unit place digit and the tenth place digit of the 2 digit number as follows

Step 2: Add the unit place digit and tenth place digit (2 + 1 = 3) and insert the sum as follows

Step 3:Repeat step 2 (2 + 1=3)and insert the sum as follows

Ans 12 x 111 = 1332

Examples

Let us see few more examples to see how this works

Example 1: 13 x 111 = ?
Step 1:Writing down unit place digit and tenth place digit with 2 blanks in between them.We get 1_ _ 3

Step 2: Adding unit place digit and tenth place digit 
we get 1 + 3 = 4
Inserting the sum in between the unit place digit and tenth place digit

we get 1_ 4 3

Step 3: Again adding unit place digit and tenth place digit 
we get 1 + 3 = 4
Inserting the sum we get 1 4 4 3

Ans  13 x 111 = 1443

Example 2:14 x 111 = ?
Step 1:Writing down unit place digit and tenth place digit with 2 blanks in between them.

We get 1_ _ 4

Step 2: Adding unit place digit and tenth place digit
we get 1 + 4 = 5
Inserting the sum in between the unit place digit and tenth place digit we get 1_ 5 4          

Step 3: Again adding unit place digit and tenth place digit 
we get 1 + 4 = 5

Inserting the sum we get 1 5 5 4

 Ans  14 x 111 = 1554

Example 3:17 x 111 = ?
Step 1:Writing down unit place digit and tenth place digit with 2 blanks in between them.

We get 1_ _ 7

Step 2: Adding unit place digit and tenth place digit
we get 1 + 7 = 8
Inserting the sum in between the unit place digit and tenth place digit we get 1_ 8 7          

Step 3: Again adding unit place digit and tenth place digit 
we get 1 + 7 = 8

Inserting the sum we get 1 8 8 7

Ans 17 x 111 = 1887

Example 4: 29 x 111 = ?
Step 1:Writing down unit place digit and tenth place digit with 2 blanks in between them.

We get 2_ _ 9

Step 2: Adding unit place digit and tenth place digit
we get 9 + 2 = 11
Inserting only the unit place digit of the sum in the blank between the unit place digit and tenth place digit . And carry forward ten’s place digit to step 3.

we get  2_ 1 9          

Step 3: Again adding unit place digit and tenth place digit 
 we get 9 + 2 = 11.

Now add carry forward from step 2(1).we get 11+1+12
Insert the one’s place digit(2) in the 3rd blank from right and carry forward ten’s place digit to step 4.

we get  2 2 1 9

Step 4: Add ten’s place digit(1) carry forwarded from step 3 to the original ten’s place digit. we get 1+2=3

Ans  29 x 111 = 3219

Example 5: 23 x 111 = ?
Step 1:Writing down unit place digit and tenth place digit with 2 blanks in between them.We get 2_ _ 3

Step 2: Adding unit place digit and tenth place digit 
we get 3 + 2 = 5
Inserting the sum in between the unit place digit and tenth place digit

we get 2_ 5 3

Step 3: Again adding unit place digit and tenth place digit 
we get 3 + 2 = 5
Inserting the sum we get 2 5 5 3

Ans  23 x 111 = 2553

Now you try multiplying the following in 5 secs
(a)15 x 111 = ?
(b)16 x 111 = ?
(c)17 x 111 = ?
(d)18 x 111 = ?

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