math tricks

Shortcut to square any number from 90 to 99

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Shortcut to square any number from 90 to 99

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.

Examples

Let us see few examples to understand better

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

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

Example 4: 96²=?

Step 1:Assuming 100 as base, we shall find the difference between the number to be squared(96) and 100.
100-96=4
We get the difference as 4

Step 2:Subtracting the difference(4) from the number to be squared(96) we get,
96-4=92
92 is the tenth place digit

Step 3:Squaring the difference we found in step 1 we get
4²=16
16 is the Unit place digit.

Ans   96²=9216

Example 5: 94²=?

Step 1:Assuming 100 as base, we shall find the difference between the number to be squared(94) and 100.
100-94=6
We get the difference as 6

Step 2:Subtracting the difference(4) from the number to be squared(96) we get,
94-6=88
88 is the tenth place digit

Step 3:Squaring the difference we found in step 1 we get
6²=36
36 is the Unit place digit.

Ans   94²=8836

Shortcut to subtract any 5 or 6 digit number in seconds

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Shortcut to subtract any 5 or 6 digit number in seconds
Shortcut to subtract any 5 or 6 digit number is a trick you can use to subtract 2 numbers in seconds.
Subtraction is the opposite of addition. Suppose we have to subtract two numbers such as 15-2=13.Then,In this subtraction the first number 15 is called the minuend meaning to be made less and the number 2 is the subtrahend meaning that which is to be subtracted and the number 13 is the difference.
Minuend-subtrahend=difference
When Minuend is larger than the subtrahend, there is no problem in subtracting.
Example:Minuend is 162 and the subtrahend is 51 and we are required to subtract the numbers.
1  6  2
–   5  1
———
1 4  1
———
We can easily get the difference whether we do it from right or left.

But what if we had to subtract 45 from 64
if we start using the method of borrowing that we are so used to from our school days no doubt we will arrive at the difference but it is not that easy.

There is a simple trick that you can use here to get the
difference easily and within seconds.

Shortcut to subtract any 5 or 6 digit steps

Lets discuss the steps now
Step 1: Subtract the numbers of the subtrahend from the Minuend 
Step 2: If any digit in subtrahend is more than Minuend then add a circle on difference you get on subtracting.
Step 3:Now wherever circle is there it means the complement of the number(10- number)
Step 4:If there is any digit before the circled number then 1 must be subtracted from the number.

We shall now consider some examples to understand better

Examples on shortcut to subtract 5 or 6 digit number 


Example 1: 47-28=?
Observe that the Minuend is 47 and Subtrahend is 28 where the unit’s place digit is more than the minuend’s units digit.
First we subtract as usual  
  4  7
– 2  8
  ———
   2 1  
  ———-      

Note that 8 is more than 7 so we add a circle on 1
We find Complement of the difference(1)=10-1=9
Subtract 1 from previous number(2) as the next digit is circled
We get 
  4 7       

 -2 8
 ———
 2  1

 1  9    


Ans  47-28=19


Example 2: 37-29=?
Minuend is 37 and Subtrahend is 29
First we subtract as usual  
        3 3
       -2 9
    ———
        1 6    

Note that the unit’s place digit(9) of subtrahend is more than the unit’s place digit(3) of minuend so we add a circle on the difference 

We find Complement of the difference(6)=10-6=4
Subtract 1 from previous number(1) as the next digit is circled
We get, 

 3 3

-2 9

 ———
 1 6
 0 4    


Ans 37-29=4


Example 3: 65381-42497=?
First we subtract as usual  

 6 5 3 8 1
-4 2 4 9 7
 —————
 2 3 1 1 6

Add circle on the digits 6,1,1 as these digits of the subtrahend are more than their corresponding digits in minuend
We get,

  6  5  3   8    1

 -4  2  4   9    7
  ———————
   2  3  1  1  6
  ———————

Now we find complements of the circled numbers 
Complement of 6=10-6=4
Complement of 1=10-1=9
Complement of 1=10-1=9

We get, 
  6  5  3  8   1
– 4  2  4  9   7
 ——————-
  2  3 9  9  4
 ——————-
Subtracting 1 from the numbers previous to the circled numbers
We get,
 6  5  3  8  1
-4  2  4  9  7
 ——————
 2  2  8  8  4
 ——————-

Ans   65381-42497=22884


Also see
What is complement of a number?

2 digit multiplication trick whose tens digit is same

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2 digit multiplication trick whose tens digit is same
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.

2 digit multiplication trick whose tens digit is same

Now,let us see the steps in detail

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

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

Example 3: 38 x 32=?
We observe that ten’s place digit of both numbers=3
and by adding unit’s place digit of both numbers(8+2=10)we get 10

Step 1:Multiplying the unit’s place digits we get
Unit’s place digit=8 x 2=16

Step 2: Multiplying ten’s place digit by its consecutive number we get
Ten’s place digit=3 x 4=12

Step 3:Placing the result of step 2 to the left of the result obtained in step 1 we get
1216

Ans  38 x 32=1216

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

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

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

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