Useful Shortcuts of Basic Maths :
Additions Shortcuts
Addition of numbers close to multiples of ten (e.g. 19, 29, 38, 59 etc.)
This technique is useful for Mental calculations
116 + 39 (Here we can write this 39 as 40-1)
= 116 + (40 - 1)
= 116 + 40 - 1
= 156 - 1 (Instead of adding 39 to 116, we just add 40 to 116 (because we can do this without using pen and paper) and later we subtract one from it)

= 155
Try this.. This is very useful tip while doing calculations.
Now lets try another example. 
116 + 97
= 116 + (100 - 3)
= 116 + 100 - 3  (Here, instead of adding 97 to 116, we are just adding a 100 to 116 and then subtracting 3 from it
216 - 3= 213
◆Addition of decimals
12.5 + 6.25
= (12 + 0.5) + (6 + 0.25) 
= 12 + 6 + 0.5 + 0.25 (Here we just added the rounded numbers first and later we added the decimal numbers :)
= 18 + 0.5 + 0.25
= 18.75
Subtractions Shortcuts
SUBTRACTION BY NUMBERS CLOSE TO 100, 200, 300, 400, ETC.
250 - 96 
= 250 - (100 - 4) (here, instead of subtracting 96 from 250, we are just subtracting 100 from 250 and then adding 4) 
= 250 - 100 + 4 (Why adding? because the actual amount we have to subtract from 250 is 96. but we are subtracting 100.

That means, we are subtracting 4 numbers more than we actually deserve. so our 250 will feel bad. so we should add that 4 to it

= 150 + 4
= 154
250 - 196
= 250 - (200 - 4) 
= 250 - 200 + 4 (here also same. In order to subtract 196, we subtract 200 and adding 4)
= 50 + 4
= 54
Note : We can use this logic for any number. According to our convenience.
Lets see, 
216 - 61 (Here i found it difficult to subtract 61 from 216)
= 216 - (100 - 39)  (So i just decided to subtract 100 to it and later will subtract the extra 39)
= 216 - 100 + 39 (Hey, see here. How about writing this 39 as 40 -1 ?)
= 116 + (40 - 1) (dont be confused. just practice this method and you will come to know how easy and efficient method it is :)
= 156 - 1
= 155
◆Subtraction of decimals
47 - 9.9 (How about dividing this 9.9 as 9 + 0.9 ??)
= 47 - (9 + 0.9)  we can write this as...
= 47 - 9 - 0.9  
= 38 - 0.9
= 37.1
18.3 - 0.8
= 18 + 0.3 - 0.8
= (18 - 0.8) + 0.3 
= 17.2 + 0.3 
= 17.5
◆Multiplication Shortcuts
Multiplication using multiples
Assume that we should find out the result of 12X15. 
12 x 15   (Here we can write this 15 as 5x3)
=  12 x 5 x 3 (now 12x5 becomes 60)
=  60 x 3 (For this you just calculate 3x6, that is 18 and add one Zero to it. that is 180)
=  180 (see, how simple it is?)
Multiplication by distribution 
Assume that we should find out the result of 12x17
12 x 17   (Here we can divide this 17 as 10+7. here, multiplying 12 with 17 is same as multiplying 12 with 10 and 7 separately and then adding the results)

so, we can write it as
= (12 x 10) + (12 x 7) 
= 120 + 84
= 204 
Multiplication by "giving and taking"
12 x 47  (Here its little difficult for us to calculate the multiplication of 12 and 47 mentally. so just check for the ROUNDED number nearer to 47. Yes it is 50. so.....

= 12 x (50 - 3) 
= (12 x 50) - (12 x 3)  (we have discussed this rule earlier)
= 600 - 36
= 564
Multiplication by 5
* If we have to multiply a number with 5, just divide the number with 2 and then multiply the result with 10. Confused? Its very simple step actually....

428 x 5   (Now just divide the number with 2)
= 428 x 1/2 = 214 (Now multiply it with 10. I mean just add a zero at the end :P)
= 214 x 10
= 2140 (This is our result)
Whats the logic behind this step? 
Very simple. 
* Lets say the number is X. 
* Now we are dividing the number with 2.  so here X becomes X/2. 
* And then we are multiplying it with 10.  So it will become 10x / 2  
* Now cancel it with 2. so it becomes 10x / 2 = 5X = 5 multiplied by X. Thats it ;)
Multiplication by 10  ------------  just move the decimal point one place to the right
16 x 10
= 160
5.9 = 159
169.93 = 169.3   (Need an explnation for this too??? :P)
Multiplication by 50 ------ divide with 2 and then multiply by 100
Well, this is also same process as we did for 5. Here we should add an extra zero. Thats it
18 x 50
= (18/2)  = 9
= 9 x 100
= 900
Multiplication by 100 -------- move the decimal point two places to the right
45 x 100
= 4500  
Multiplication by 500-------- divide with two and multiply with 1000 
21 x 500
= 21/2 x 1000
= 10.5 x 1000
= 10500
Multiplication by 25 ---------- use the analogy Rs 1 = 4 x 25 Paise
25 x 14 (just divide the 14 as 10+4)
= (25 x 10) + (25 x 4) 
= 250 + 100 --->  Rs2.50 + Rs1
= 350
Hey one more thing. Here you can use another technique too. Which we have used for multiplication with 5.
Multiplication by 25 -----------  Divide by 4 and multiply by 100 
36 x 25
= (36/4) x 100
= 9 x 100
= 900  
Multiplication by 11 (if sum of digits is less than 10)
72 x 11
= 7+2 =9, it is Less than 10. so,
= place this term 9 between 7 &2
= 792 (That's the answer)
Multiplication by 11 (if sum of digits is greater than 10)
87 x 11
=>  8 + 7 = 15 
because here 15 is greater than 10, first use 5 and then add 1 to the first term 8, 
which gives you the answer
= 957 
Multiplication of numbers ending in 5 with the same first terms (square of a number)
25 x 25 
first term = (2 + 1) x 2 = 6
last term = 25
answer = 625 ---> square of 25
75 x 75 
first term = (7 + 1) x 7 = 56
last term = 25
answer = 5625 ---> 75 squared
◆Division Shortcuts
Division by parts --> Imagine you have Rs.874 . You have to give that to your two children.
874/2    [We can write this 874 as 800+74 (for our convenience)
= 800/2 + 74/2
= 400 + 37
= 437 
Division using the factors of the divisor: "this is also called as Double Division"
70/14
= (70/7)/2    (Because 7 and 2 are the factors of 14)
= 10/2
= 5
Division using Fractions:
132/2
= (100/2 + 32/2) ( here we've broken the given fraction into two separate fractions)
= (50 + 16)
= 66
Division by 5 :
Note: if you have to divide any number with 5, then divide it by 100 and then just multiply by 20
1400/5
= (1400/100) x 20
= 14 x 20
= 280
Division by 10 (Its very simple, just move the decimal point one place to the left)
0.5/10
= 0.05 
Division by 50 ( Just divide with 100 then multiply by 2)
2100/50
= (2100/100) x 2
= 21 x 2
= 42
700/50
= (700/100) x 2
= 7 x 2
= 14
Division by 100 (just move the decimal point two places to the left)
25/100 
= 0.25
Division by 500 (just divide with 100 and then multiply with 0.2)
17/500 
= (17/100) x 0.2 
= 0.17 x 0.2
= 0.034
Division by 25 (just divide by 100 and then multiply by 4 )
500/25
= (500/100) x 4
= 5 x 4
= 20
750/25
= (750/100) x 4
= 7.5 x 2 x 2
= 30 
◆Decimals
1% = 1/100 = 0.01   (if two zeros are given, just move the decimal pointer two places left)
2% = 2/100 = 0.02 = 1/50 (the simplification of 2/100)
3% = 3/100 = 0.03 
4% = 4/100 = 0.04 = 1/25
5% = 5/100 = 0.05 = 1/20
6.25% = 6.25/100 = 0.0625 = 1/16 
7% = 7/100 = 0.07
7.5% = 7.5/100 = 0.075
10% = 10/100 = 0.1 = 1/10
12.5% = 12.5/100 = 0.125 = 1/8
20% = 0.2 = 1/5 
21% = 0.21
25% = 0.25 = 1/4
30% = 0.3 = 3/10
33.33% = 33.33/100 = 0.3333 = 1/3
37.5% = 0.375 = 3/8
40% = 0.4 = 2/5
50% = 0.5 = 1/2
60% = 0.6 = 3/5
62.5% = 0.625 = 5/8
66.66% = 66.66/100 = 2/3
75% = 0.75 = 3/4
80% = 0.8 = 4/5
87.5% = 0.875 = 7/8
100% = 1
125% = 1.25 = 1 1/4
150% = 1.5 = 1 1/2
200% = 2