Maths Shortcut Tricks 2018 @In Just 10 Seconds


October 23, 2018

 

               Maths Shortcut Tricks 2018 @In Just 10 Seconds  

           

     

   By ALOK SRIVASTAVA

 

 

  1. Two Digit Multiplication

 

Rule 1.

(a)                             98 × 99 = 9702

 

Sol :   100 – 98 = 2

100 – 99 = 1

2 + 1 = 3

100 – 3 = 97

2 × 1 = 2

Since, Answer would be in 4 digits

so, 98 × 99 = 9702 .

 

 

  • (b)                         94 × 93 = 8742

Sol:

100 – 94 = 6

100 – 93 = 7

94 – 7= 87, 93 – 6 = 87

So, we choose 87 once in answer

Now, 6 × 7 = 42

So, final answer would be 8742.

 

Rule 2

 

  • (a)                 32 × 46 = 1472

  • Let A = 2 and B = 6 , C = 3 and D = 4

  • A × B

  • B × C + D × A

  • Add carry Numbers, if it is

  • C × D add carry numbers

See,

  • 2 × 6 = 12

  • Write 2 at once place and carry over is1.

  • 6 × 3 + 4 × 2 = 26

  • Add 1. 26 + 1 = 27

  • Write 7 at ten’s place and carry over is 2

  • Then 3 × 4 = 12

  • 12 + 2 = 14

  • Now we will have 1472

  1. Three Digits Multiplication

 

Rule 1.

 

 

103 × 105 =

  • 103 – 100 = 3

  • 105 – 100 = 5

  • 103 + 5 = 108, 105 + 3 = 108

  • We choose 108 once in answer

  • And 5 × 3 = 15

  • Final answer be 10815

Rule 2.

 

Any three digits Multiplication

 

472 × 389 =

  • Let A = 2 , B = 9, C = 8 , D = 7, E = 4 and F = 3

  • A × B

  • B × C + D × A

  • Add Carry numbers, if it is

  • B × E + F × A + C × D

  • Add carry over numbers, if it is

  • C × E + F × D, add carry numbers

  • E × F and add carry numbers

  • See,

 

  • 2 × 9 = 18

  • Write 8 at one’s place and carry over is1

  • 9 × 7 + 8 × 2 = 79

  • 79 + 1 = 80

  • Write 0 at ten’s place and carry over is 8

  • 9 × 4 + 3 × 2 + 8 × 7 = 98

  • 98 + 8 = 106

  • Write 6 at hundred place and carry over is 10

  • 8 × 4 + 3 × 7 = 53

  • 53 + 10 = 63

  • Write 3 at thousand place and carry numbers is 6

  • 4 × 3 = 12

  • Add 12 + 6 = 18

  • Now we will have 183608

 

  1. Mixed Digits Multiplication

 

Rule 1

 

 

104 × 98 =

  • 104 – 100 = 4

  • 100 – 98 = 2

  • 98 + 4 = 102, 104 – 2 = 102

  • So, we choose 102 once in answer

  • We will write 10200 first

  • Then subtract 4 × 2 = 8 from 10200

  • Now, we have 10200 – 8 = 10192

Rule 2

 

314 × 67 =

  • Let A = 3, B = 1, C = 4, D = 0, E = 6 and F = 7

  • C × F

  • B × F + E × C

  • F ×A + D × C + B × E

  • A × E + D × B

  • A × D

  • Now, we will have an answer

314 × 67

  • Let A = 3, B = 1, C = 4, D = 0, E = 6 and F = 7

  • 4 × 7 = 28, take 8 as a unit place and carry over number is 2

  • 1× 7 + 6 × 4 = 31

  • Add 2 to 31 means 2 + 31 = 33

  • Take 3 as a ten’s place and carry number is 3

  • 7 × 3 + 0 × 4 + 1 × 6 = 27

  • 27 + 3 = 30 (3 is carry number)

  • Take 0 as a thousand place and carry number is 3

  • 3 × 6 + 0 × 1 = 18

  • 18 + 3 = 21

  • Now answer would be 21038

Short cut to find Square of any Number

 

 

      Square of  any Two Digits

 

 

  • Square of 47

  • Square of 7 is 49

  • We will write 9 at unit place and carry over is 4

  • Then 4 × 7 × 2 = 56 and add 4 it becomes 60

  • Put 0 at ten’s place and carry over is 6

  • Square of 4 is 16 then add 6

  • 16 + 6 = 22

  • Now we will have 2209

  • Square of any three Digits

 

Square of 215

 

  • We will add 15 and subtract 15 for getting 200and 230

  • Square of 15 is 225

  • Choose 25 and carry over number is 2

  • Subtract 15 from 215, we will have 200 and adding 15 to 215, we will have 230

  • Then (200 × 230) ÷ 100 = 460

  • Add 460 + 2 ( 2 is carry over)= 462

  • Put 25 after 462

  • Now, we will have 46225

Square  of  643

 

  • We will add 7 and subtract 7 for getting 650 and 636

  • Square of 7 is 49

  • Then (650 × 636) ÷ 100 = 4134

  • Put 49 after 4134

  • Now we will have 413449

Square Root of a Number

 

 

Square Root of √5329 =

 

 

  • Unit place digit can be 3 or 7

  • Focus first two digit 53

  • 53 comes between 72 = 49 and 82 = 64

  • So we will take small digit 7 at ten’s place

  • Now for unit digit, 7 and just after 8 we multiply 7 × 8 = 56

  • Since 53 is less than 56 so, unit place would be 3

  • Now answer would be 73.

  • Square root of   6724

 

  • Square of 2 is 4 and square of 8 is 64 so may be 2 or 8 at unit place

  • 67 comes between 64 and 81 which is square of 8 and 9

  • Then focus 67 which is near by 64 and it is square of 8

  • Answer would be 82

Square Root of 47961

 

 

  • Unit place digit can be 1 or 9

  • Now, consider 479

  • Square of 22 is 484 which is greater than 479 so take square of 21 = 441

  • Take 21 in first place

  • Now talking about unit place

  • Here we multiply 21 × 22 = 462

  • Since 479 is greater than 462 so take 9 as a unit place

  • Now answer would be 219

 

Cube of Two Digits Number

 

  • (12)3 =

  • Let A = 1 and B = 2

  • Write  A    B         B2         B3

+      2×B    2× B2

      A  B + 2 × B    B2 + 2 × B2  B3

So, (12)3 =     1   2  4  8

+      4   8

                  1  7   2   8

 

Cube Root of a Number

 

 

Cube Root of √ 59319   =

 

  • We will take unit place digit 9 as it

  • Now focus first two digit 59

  • 59 comes between 33 = 27 and 43 = 64

  • So we will take small digit 3 at ten’s place

  • Then answer would be 39

Cube Root of √157464 =

 

  • We will take unit place digit 4 as it

  • Now focus first three digit 157

  • 157 comes between 53 = 125 and 63 = 216

  • So we will take small digit 5 at ten’s place

  • Then answer would be 54

Trick to Learn Table (2 to 100)

 

 

  • Here, I am not talking about table from 2 to 9 as it is very easy to learn.

Table of 12

 

 

  • See, we can take any table. So let’s talk about table of 12 first

  • Here 2 s one’s place and 1 is ten’s place

  • So when we talk about 12 × 7

  • Remember, we are not going to multiply 7 × 2 = 14 first

  • First of all, we will observe 12 as 10 + 2

  • Now we multiply 7 × 10 first and it becomes 70

  • And then 2 × 7 = 14

  • Now, 70 + 14 = 84.

Important Note: You can apply the same method on table of 12 to 99

 

 

  Next example table of 74

 

  • Suppose 74 × 8 =

  • We can see 74 as 70 + 4

  • We will do 70 × 8 first

  • It becomes 560

  • Then we multiply 4 × 8 = 32

  • Now , 560 + 32 = 592

 

Digital Root Method

 

Digital Root means sum of all the digits should be equal to single digit. In this case, 9 is always equal to zero.

 

  • Example: 2567

Sum of this number 2 + 5 + 6 + 7 = 20

Again 2 + 0 = 2

Here we have single digit 2

So, this is a digital method.

 

  • Example 2053 +232 +1965 + 654 = ?

  • (a) 4904

  • (b) 3954

  • (c) 3636

  • (d) 2335

Solution : 2053 = 2 + 0 + 5 + 3

= 10

= 1+ 0

= 1

232 = 2 + 3 + 2

= 7

1965 = 1 + 9 + 6 + 5

1 + 0 + 11

= 12

1+ 2

= 3

654 = 6 + 5 + 4 = 6 + 9

6 + 0

= 6

Now total would be 1 + 7 + 3 + 6

= 1+ 7 + 9

= 8 + 0

= 8

 

CORRECT  OPTION is (b) as 4904

= 4 + 9 + 0 + 4

= 4 + 0 + 0 + 4

= 8

 

 

  • Example : (86)2 = ?

  • (a)

  • ( a) 6386

  • (b) 7396

  • (c) 8366

  • (d) 7346

Solution : (86)2 = 86 × 86

8 + 6 × 8 + 6

= 14 × 14

= 1 + 4 × 1 + 4

= 5 × 5

= 25

= 2 + 5

= 7

 

OPTION (b) is CORRECT as 7396

7 + 3 + 9 + 6

= 7 + 9 + 0

= 7 + 0 + 0

= 7

 

 

Division Trick Using Digital Sum

 

 

Important note: in digital case, 9 is always equal to 0 .

 

  1. 25 ÷ 2345 =  ?

  • 350

  • 450

  • 250

  • 750

Let’s start

340025 = 2345 × X

3 + 4 +0 + 0 +2 + 5 = 2 + 3 + 4 + 5 × X

9 + 5  = 9 + 5 × X

0 + 5 = 0 + 5 × X

5 = 5 × X

Now X = 1

Now focus on Option (a)

  • 350 = 1 + 3 + 5 + 0

= 9 + 0

= 0

  • 450 = 1 + 4 + 5 + 0

= 1 + 9

= 1 + 0

= 1

 

So answer would be 1.450

 

Division By Short cut Method

 

 

                                                        (a)                  478 / 5

= (478 × 2) / 5 × 2

= 956 / 10

= 95.6

                                                           (b)            232 / 25

=    (232 × 4) / 25 × 4

=     928 / 100

=    9.28

                                                                  (c)        118 / 125

=   (118 × 8) / 125 × 8

= 944 /1000

= 0.944

 

Maths Magical Tricks

 

  1. Value of √2 + √2 + √ 2 + √ 2 +………….Infinite

Solution :  (√4a + 1   + 1) / 2

Here,       a = 2

So answer be   ( √4 × 2 + 1    + 1)/ 2

(3 + 1) / 2

= 2

 

 

 

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