How to improve calculation speed with shortcut-tricks

Calculation speed plays a very very important role in All Competitive Exams.Some peoples have natural ability to do the calculation fast  but that doesn't mean the ordinary people like me and you can't on that level.But the solution is only practice.Here i am providing you all basic things which will help you  to improve your calculation speed.

Some recommended things are mentioned here which you must do it before starting.

30 x 30-Just spend 30 minutes a day for 30 days. You will definitely find the difference in your calculation speed.Practice involves basic  Multiplications, Additions, Subtractions,Percentage Calculations,Comparing Fractions and Calculating Squares.

Click the below links to get content accordingly..

1-Multiplication Tables (Up to 20 x 20)

2-Squares (Up to 50)

3-Cubes (Up to (20)

4-Powers of 2 (Up to 14)

5-Powers of 3 (Up to 6)

6-Some Useful Shortcuts of Basic Maths :                    a)   Addition Shortcuts                                  Addition Mentally (Without Using Pen and Paper)                                 Addition Shortcuts                  b)  Subtraction Shortcuts                                Subtraction  Mentally (Without Using Pen and Paper)                                Subtraction Shortcuts                  c)  Multiplication Shortcuts                  d)  Division Shortcuts                  e)  Decimals

7-Reciprocals of numbers (Up to 13)

8-Complements of 100 ( means the difference between 100 and the given 2 digit number)

1. 
   

Mental Maths Subtraction

Here i an going to show you that how to do Subtractions Mentally. Have a look at the following example..

Example-1
586-331=? subtractions would be faster by taking two digits instead of taking a single digit at a time. Always start from right side and take two digit. So take 86 and 31 86 - 31 = 55 500 - 300 = 200 So, the result of 586-331= 255

Example-2
756-385=? By taking two digits instead of taking a single digit at a time, Starting from right side and take two digit. So take 56 and 85 here 56<85 so we will borrow 1 from 7 and 56 becomes 156 (called complement of 100's) now subtract 156-85 = 71 So, the result of 756- 385 =371

Example-3
730 - 156 + 523 - 814 = ? when we have addition and subtraction both in single equation than first we add + signs number and in second part add - sign numbers  i.e  (730 + 523)-(156 + 814)      =1253 - 870 // apply example-2 rule because z 53<80.Borrow 1 from 12      =383

Mental Maths For Additions

Now, we are going to show you how to do Additions Mentally. Have a look at

                                                     Example-1

425 + 336 + 927+ 811 + 222 = ?

while adding three-digit numbers, first add-two-digits at a time (Units and Tens Place). 25 + 36 + 27 + 11 + 22 = 121 To add 25 and 36, mentally treat 25 as 20 + 5 and 36 as 30 +6 So, 20 + 30 = (20 + 30) + 5 + 6 = 61 Similarly, 61 + 27 = (60 + 20 + 7 + 1 = 88 88 + 11 = (80 +10) + 8 + 1  = 99 99 + 22 = (90 + 20) + 9 +2 = 121 The last two digits (the units place and the tens place) of the addition are 21, while the digit 1 is to be carried forward). Now Add, 1 (Carried) + 4 + 3 + 9 + 8 + 2 = 27 So, the answer of the above addition is 2721 (initially, it may look confusing. Just practice this method and you can find how efficient this method is :  The same logic can be extended to 4 digit additions too... have a look

Example-2

3425 +4336 + 2927 + 811 + 4222 = ?

Now, we are going to show you how to do Additions Mentally. Have a look at 3425 +4336 + 2927 + 811 + 4222 Part-1 25 + 36 + 27 + 11 + 22+ ? while adding three-digit numbers, first add-two-digits at a time (Units and Tens Place). 25 + 36 + 27 + 11 + 22 = 121 To add 25 and 36, mentally treat 25 as 20 + 5 and 36 as 30 +6 So, 20 + 30 = (20 + 30) + 5 + 6 = 61 Similarly, 61 + 27 = (60 + 20 + 7 + 1 = 88 88 + 11 = (80 +10) + 8 + 1  = 99 99 + 22 = (90 + 20) + 9 +2 = 121 The last two digits (the units place and the tens place) of the addition are 21, while the digit 1 is to be carried forward). Part-2  Now Add, 1 (Carried) + 34 + 43 + 29 + 8 + 42 = 277 30 + 40 +20 + 40 + 1 (carry) +4 + 3 + 9 + 8 + 2 =157 So, the answer of the above addition is 15721 . The same logic can be extended to 5 , 6 , 7 and so on digit additions too.

Reciprocals of numbers up to 13

1/2	0.5
1/3	0.333
1/4	0.25
1/5	0.20
1/6	0.166
1/7	0.143
1/8	0.125
1/9	0.111
1/10	0.1
1/11	0.091
1/12	0.083
1/13	0.077

Division Short-Cut Trick

Division by using fractions	Division by 5
132/2 = (100/2 + 32/2) ---> break down into two fractions = (50 + 16) = 66	1400/5 = (1400/100) x 20---> divide by 100 then multiply by 20 = 14 x 20 = 280
Division by 10	Division by 50
0.5/10 = 0.05 ---> 5% is 50% divided by ten	2100/50---> divide by 100 then multiply by 2 = (2100/100) x 2 = 21 x 2 = 42

Division by 100	Division by 500
25/100---> move the decimal point two places to the left = 0.25	17/500 = (17/100) x 0.2---> divide by 100 then multiply by 0.2 = 0.17 x 0.2 = 0.034
Division by 25	Division by parts
500/25 ---> divide by 100 then multiply by 4 = (500/100) x 4 = 5 x 4 = 20	Imagine dividing $874 between two persons 874/2 = 800/2 + 74/2 = 400 + 37 = 437
750/25---> divide by 100 then multiply by 4 = (750/100) x 4 = 7.5 x 2 x 2 = 30	Division using the factors of the divisor: "double division" 70/14 = (70/7)/2 ---> 7 and 2 are the factors of 14 = 10/2 = 5

Addition and Subtraction Of Decimals

Example-1	Example-2
13.5 + 7.25 = (13 + 0.5) + (7 + 0.25) = 13 + 7 + 0.5 + 0.25 (Here we just added the rounded numbers first and later we added the decimal numbers :) = 21 + 0.5 + 0.25 = 21.75	200.57 + 21.25 = (200 + 0.57) + (21 + 0.25) = 200 + 21 + 0.57 + 0.25 (Here we just added the rounded numbers first and later we added the decimal numbers :) = 221 + 0.57 + 0.25 = 221.82
Example-3	Example-4
490.975 + 21.231 = (490 + 0.975) + (21 + 0.231) = 490 + 21 + 0.975 + 0.231 (Here we just added the rounded numbers first and later we added the decimal numbers and forward carry if any :) = 511 + 1.206 = 512.206	590.975 - 20.231 = (590 + 0.975)  -(20 + 0.231) = (590 - 20) + (0.975 - 0.231) (Here we just added the rounded numbers first and later we added the decimal numbers ) = 570 + 0.744 = 570.744

Example-5
12.5 + 6.25 = (12 + 0.5) + (6 + 0.25) = 12 + 6 + 0.5 + 0.25                                                                           //add the integers then the decimals = 18 + 0.5 + 0.25 = 18.75

Test-YourSelf:  
1-     215.55  +  28.67
2-    197.88   + 98.300
3-    587.91   +  109.105
4-    856.87  +   456.009
5-    566-76  -   45.25
6-    456.156  -  56.100
7-    9956-786  - 567.567
9-    4444.555 - 3456.921
10-  234.67    -   100.360

Subtraction Shortcuts

Recommended -Calculate Mentally (Don't use pen, paper and pencil)

It is very useful tip.Just take it in your habit.

Example-1	Example-2
216 - 87  (Take last 2 digits at a time from both numbers .If left 2 digit is less then 2 digit of right side than borrow 1 from neighbor.Here 16<87 so 16 can borrow 1 from his neighbor i.e from 2.Now we can write 16 as 116 ) = 100 +116-87 (neighbor is now 2-1=1) =  100+29 = 129	510 - 296  Take last 2 digits at a time from both numbers .If left 2 digit is less then 2 digit of right side than borrow 1 from neighbor.Here 10<96 so 10 can borrow 1 from his neighbor i.e from 5.Now we can write 10 as 110 ) =400+(110-96)-200 =200+14 =+214
Example-3	Example-4
250 - 97 = 250 - (100 - 3) = 250 - 100 + 3   // subtract 100 then add 3 = 150 + 3 = 153	250 - 197 = 250 - (200 - 3) = 250 - 200 + 3      // subtract 200 then add 3 = 50 + 3 = 53

Example-5
216 - 61 = 216 - (100 - 39)                                                                                                                                     = 216 - 100 + 39 = 116 + (40 - 1) = 156 - 1 = 155

 Practice Time:

Recommended-Do it in 3 min

1-     215  -  28
2-    197   -  88
3-    587   -  91
4-    856   -  87
5-    566   -  76
6-    456   -  156
7-    9956  -  786
9-    4444  -  555
10-  234    -   67

Addition Short-Cut Trick

Recommended -Calculate Mentally (Don't use pen, paper and pencil)

It is very useful tip.Just take it in your habit.

Method-1

Example-1	Example-2
216 + 87  (Take last 2 digits at a time from both numbers .Here we can write 16 as 20-4 and  87 as 90-3) = (20-4) + (90 - 3) (and add carry with 2) =  (20+90)-(4 +3) = (110)-7  (carry is 1 in 110.So add 1 with 2  ) = 03 (put 3=1+2 at third place) =303	296 + 510  (Take last 2 digits at a time from both numbers .here we can write 96 as 100-4 and  10) = 96+10 (and add carry with 5 and 2) = 106 (carry is 1 in 110.So add 1 with 2 and 5 in next step  ) = 06 (put 2+5+1 (carry) at third place) =806

Method-2-Take a look

Example-3	Example-4
116 + 29   ( we can write this 29 as 30-1) = 116 + (30 - 1) = 116 + 30 - 1 = 146 - 1 (Instead of adding 29 to 116, we just add 30 to 116  we can do this without using pen and paper and later we subtract one from it) = 145	341 + 71  (here we can write this 71 as 71+1) = 341 + (70 +1) = 341 + 70+1 (Here, instead of adding 70 to 341, we are just adding a 70 to 341 and then add 1 ) = 411+1 = 412
Example-5	Example-6
116 + 38 = 116 + (40 - 2) = 116 + 40 - 2 ---> add 40 then subtract 2 = 156 - 2 = 154	116 + 98 = 116 + (100 - 2) = 116 + 100 - 2 ---> add 100 then subtract 2 = 216 - 2 = 214

Practice Time:

Recommended-Do it in 3 min
1-     215  +  28=
2-    197   +  88=
3-    587   +  91=
4-    856   +  987=
5-    566   +  76=
6-    456   +  56=
7-    56     +  786=
9-    444   +  555=
10-  234   +  67=

Power of 3 up to 6

Power Of 2 Up To 14

Cubes Up To 20

Squares Up To 50

Table Up To 20

Do Practice:

3* 7=                  8* 3 =                         9 *3 =              7* 5=              7*  15=
6 * 5 =               11*6=                          9 *2 =              6 * 3=             11 * 11=
3 *8 =                 9 *13=                        2 *7=               7 * 4 =            7 * 12 =  
4 *3=                  3* 11 =                       13*12=            7 * 3 =            4 *  8 =   
5  * 9=               12 *13=                       9 *  6=            8 * 8 =             15 *13 =  
6  * 2 =                4  *  6=                      14 * 6=           7  * 8 =             8 * 11=   
7 *  8 =                5  *  3=                     15 * 13 =          5 * 2=              6  *  7 = 
8 *13=                 3  *  9=                     8 * 13  =          4 *  6 =             9 *15 =
9 *  6=                 7  *  4 =                    5 *   8  =          8 * 4 =            12  *  9=      
10  * 2=               7  *  6=                     3   * 7=            13 * 5=           14  *  3=
11 *  7=               12  *12=                   4 *   6=           15 * 3 =           11 *   3=

12 *  2=               12  *11=                   7   * 9=            8  *9  =            6  *  3 =