Math Trick

What is complement of a number

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What is complement of a number
What is complement of a number

The distance of a number from a convenient round number(base) or how far the number is from its base is known as the complement of a number.
Numbers such as 10,100,1000 are usually taken as bases as they are friendly numbers.
It is a simple concept but very helpful when you apply this concept to solve problems.
Suppose you want to substract two difficult numbers then if you know the complement of the numbers then you will be surprised to see how quickly you can mentally calculate the answer.

Let us now find out the complements of numbers taking different bases.

First lets start finding complement of numbers from 1 to 9 with 10 as base
10-1=9
9 is a complement of 1

10-2=8
8 is a complement of 2

10-3=7
7 is a complement of 3

10-4=6
6 is a complement of 4

10-5=5
5 is a complement of 5

10-6=4
4 is a complement of 6

10-7=3
3 is a complement of 7

10-8=2
2 is a complement of 8.

10-9=1
1 is a complement of 9.

Now lets take the base as 100 and find complements of numbers

To find the complement of a number with 100 as base follow the below steps
For the unit’s place digit find the complement of the units place digit with 10 as base
For the ten’s place digit find the complement of the ten’s place digit with 9 as base

We shall now practice few examples to perfect the skill that we learnt
100-11=?
Steps
For the unit’s place digit find the complement of 1 with base 10 (10-1=9)
For the ten’s place digit find the complement of 1 with base 9 (9-1=8)

Ans 100-11=89

100-21=?
Unit’splace digit=Complement of 1 with base 10 is 9(10-1=9)
Ten’s place digit=Complement of 2 with base 9 is 7(9-2=7)

Ans 100-21=79

100-42=?
Unit’splace digit=Complement of 2 with base 10 is 8 (10-2=8)
Ten’s place digit=Complement of 4 with base 9 is 5 (9-4=5)

Ans 100-42=58

Now lets take the base as 1000 and find complements of numbers

To find the complement of a number with 1000 as base follow the below steps
For the unit’s place digit find the complement of the units place digit with 10 as base
For the ten’s place digit find the complement of the ten’s place digit with 9 as base
For the hundreth’s place digit find the complement of the hundreth’s place digit with 9 as base

We shall now practice some examples
1000-121=?
Unit’splace digit=Complement of 1 with base 10 is 9 (10-1=9)
Ten’s place digit=Complement of 2 with base 9 is 7 (9-2=7)
Hundreth’s place digit=Complement of 1 with base 9 is 8 (9-1=8)

Ans 1000-121=879

1000-472=?

Unit’splace digit=Complement of 2 with base 10 is 8 (10-2=8)
Ten’s place digit=Complement of 7 with base 9 is 2 (9-7=2)
Hundreth’s place digit=Complement of 4 with base 9 is 5 (9-4=5)

Ans 1000-472=528

Note
If the unit’s place is 0 then Ignore the 0 and start finding the complement of the number from the next digit.
For example lets say we want to find the complement of 220
1000-220=?
Unit’s place digit=0
Ten’s place digit =Complement of 2 with base 10 is 8 (10-2=8)
Hundreth’s place digit=Complement of 2 with base 9 is 7 (9-2=7)

Ans 1000-220=780

1000-470=?
Unit’s place digit=0
Ten’s place digit =Complement of 7 with base 10 is 3 (10-7=3)
Hundreth’s place digit=Complement of 4 with base 9 is 5 (9-4=5)

Ans 1000-470=530

More Math tricks>>

3 digit multiplication trick in banking

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3 digit multiplication trick in banking
3 digit multiplication trick


A person who knows math tricks certainly has an edge over the others.With the ability to rapid do mental calculation one will not only be able to score higher marks in competitive exams but will also enhance his mental sharpness enormously. Its fun to calculate this way after all, steps of calculation need not be shown on paper!




Below we shall discuss one such multiplication trick wherein you will be able to multiply any two 3 digit numbers easily within seconds.
One thing to remember here is that both the numbers should be close to 100.The closer they are the easier it is to multiply.

Here are steps to do the 3 digit multiplication in detail

Step 1:Find the difference of each of the numbers from 100
Step 2:Multiply the differences that you found in step 1 to get the unit’s place digit
Step 3:Add the differences of both the numbers to 100 and place them to the left of the result obtained in step 2.

Let us now consider an example to understand better

Example 1: 102 x 103
Here we notice that both the numbers are close to 100
We shall apply the technique that we learnt 

Step 1:First we find the differences of the numbers
We observe that 
102 is 2 more than 100 so the difference is 2
103 is 3 more than 100 so the difference is 3

Step 2:Multiplying the differences 
we get,
2 x 3=6 which is the unit’s place digit.

Step 3:Now to find the rest of the number adding the differences to 100 
we get,
2+3+100=105

Placing 105 to the left of the result obtained in step 2(6)
we get 
102 x 103=10506

Ans 10506


Try multiplying the below numbers using the above trick and see how fast you are able to do it
(1)101 x 102
(2)102 x 104
(3)103 x 104
(4)104 x 105
(5)105 x 106
(6)106 x 107
(7)107 x 108
(8)108 x 109

Shortcut to square any number from 100 to 120

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Shortcut to square any number from 100-120
Shortcut to square any number from 100 to 120 using base method. Base method is popularly used to find square of numbers when the numbers are close to a base.By choosing the right base you will arrive at your answer quickly.
So whenever you see 102,101,112,106 it should strike to you immediately .


Hey! this is quite close to 100 so let me take the base as 100 and see if I can get the answer soon.

Here we discuss the shortcut method to square any number from 100 to 120 using the base method.

Lets go through the steps now

Examples

Example 1: Find square of 102 in seconds?

Step 1:Take 100 as base and see how far the number is from 100.
Add the given number and its deviation.
Lets say you need to square 102.
Here you can notice that the number is 2 more than 100.
Adding the given number(102) and its deviation(2)
we get,
102+2=104

Step 2:Square the deviation(2)and place it next to the result obtained in step 1.
Squaring we get,
22=4

Ans 10404

Example 2: Find square of 103 in seconds?

Step 1:Take 100 as base and see how far the number is from 100.
Add the given number and its deviation.

Here you can notice that the number is 3 more than 100.
Adding the given number(103) and its deviation(3)
we get,
103+3=106

Step 2:Square the deviation(3)and place it next to the result obtained in step 1.
Squaring we get,
32=9

Ans 10609

Example 3: Find square of 104 in seconds?

Step 1:Take 100 as base and see how far the number is from 100.
Add the given number and its deviation.

Here you can notice that the number is 4 more than 100.
Adding the given number(104) and its deviation(4)
we get,
104+4=108

Step 2:Square the deviation(3)and place it next to the result obtained in step 1.
Squaring we get,
42=16

Ans 10816

Vedic math trick to check multiplication

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Vedic math trick to check multiplication

Vedic maths is the ancient mathmematics discovered from the vedas by Sri Bharati Krsna Tirthaji. My Salutations to the Swamiji for providing us with such a useful and magical tool to solve complex mathematical problems. Vedic math trick to check multiplication is one such amazing trick. This Vedic math trick is an easy method to check if the multiplication of any two given numbers is done correctly.

Vedic math trick to check multiplication steps

Let us now see the how it is done in the steps below.

Step 1:Find the sum of the digits of the numbers to be multiplied separately.

Step 2:Find the sum of the digits of the answer you got on multiplying each of the numbers.

Step 3:Multiply the results obtained in step 1 and find its sum of digits.

Step 4:Compare the sum of digits obtained in step 2 with the sum of the digits obtained in step 3.
If both are same then it means you have multiplied correctly.

Examples
Let us consider an example to understand better

Example 1: 105 x 140=14700
We want to check whether 14700 is the correct answer.
Here is how we can check it
Step 1:Finding sum of the digits of 105
         105=1+0+5=6
         Finding sum of digits of 140
         140=1+4+0=5
Step 2:Finding sum of digits of the answer 14700
          14700=1+4+7+0+0=12=1+2=3

Step 3:Multiplying the results obtained in step 1 we get,
          6 x 5=30
        finding sum of digits of 30
        30=3+0=3

Step 4:Comparing result obtained in step 2 with result obtained in step 3 we notice that
Sum of digits in the both the cases is 3.

Hence, we can conclude that our multiplication is right and we arrived at the correct answer.



Shortcut to divide 2 digit number by 5

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Shortcut to divide any 2 digit number by 5

Shortcut to divide 2 digit by 5 is an amazing trick you can use to get answer in seconds. Speed with accuracy makes the difference between success and failure in competitive exams.

Shortcut to divide 2 digit by 5 steps

Let us see the steps on how to divide any number by 5

Step 1: Double the given number.

Step 2: Shift the decimal point to the left by one place.

Now we shall practice some examples using this trick

Examples

Example 1: 42/5=?
Step 1:By doubling 42 we get 84.

Step 2:By shifting the decimal point to the left by one place we get 8.4

Ans  42/5=8.4

Example 2:18/5=?
Step 1: By doubling 18 we get 36.

Step 2: By shifting the decimal point to the left by one place we get 3.6

Ans  18/5=3.6

Example 3:24/5=?
Step 1: By doubling 24 we get 48.

Step 2: By shifting the decimal point to the left by one place we get 4.8

Ans  24/5=4.8

Example 4: 73/5=?
Step 1: By doubling 73 we get 146.

Step 2: By shifting the decimal point to the left by one place we get 14.6

Ans  73/5=14.6

Example 5: 37/5=?
Step 1: By doubling 37 we get 74.

Step 2: By shifting the decimal point to the left by one place we get 7.4

Ans  37/5=7.4