Mental Maths (Subtractions)

In this post, we will show you how to do Subtractions Mentally. Have a look at the following examples....

• 987 - 256 = ?

• Instead of taking a single digit at a time, subtractions would be faster by taking two digits.... See here
• 87 - 56 = 31
• 900 - 200 = 700
• So, the result of 987 - 256 = 731

• 824 - 587 = ?

• Take 100s Complement of 87 (i.e. 100 - 87) which is 13 and add it to 24. The result is 37. This gives the units and tens digits of the result. Since 24 < 87, we have actually subtracted 87 from 124 i.e. we have borrowed 1 from 8 ( of 824). So, we now do (7-5) = 2. The result is 237. (For new learners, this technique may look lil confusing. If you feel it is confusing, then just read it for two times and try to understand the logic behind it).

• 9217 - 858 = ?

• Adding 100s complement of 58 (which is 42, i mean 58 + 42 = 100) to 17, we get (42+17) = 59 which gives the units and 10s digits of the result. 
• Since 58 is greater than 17, we have to borrow 1 from 92 which leaves us with 91.  So, the first part of the answer is 91 - 8 = 83. SO, the result is 8359.

• 934 - 286 + 847 - 798 = ?

• When we have a combination of additions and subtractions, first add all the numbers with + sign before them and add all the numbers with - sign before them. 
• I mean (934 + 847)  - (286 + 798) = 1781 - 1084
• By applying the method explained in previous examples, 1781 - 1084 = 697.

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00:17 - By Unknown 0

 Mental Maths (Additions)

In this post, we will show you how to do Additions Mentally. Have a look at the Following Examples........

• 342 + 557 + 629 + 746 + 825 = ?

• When we are adding three-digit numbers, first add-two-digits at a time (Units and Tens Place).
• 42 + 57 + 29 +| 46 + 25 = 199
• To add 42 and 57, mentally treat 57 as 50 + 7 ( Because 50 would facilitate quick addition)
• So, 42 + 57 = (42 + 50) + 7 = 92 + 7 = 99
• Similarly, 99 + 29 = (99 + 20_ + 9 = 128
• 128 + 46 = (128 + 40) + 6 = 174
• 174 + 25 = (174 + 20) + 5 = 199
• The last two digits (the units place and the tens place) of the addition are 99, while the digit 1 is to be carried forward).
• Now Add,
• 1 (Carried) + 3 + 5 + 6 + 7 + 8 = 30
• So, the answer of the above addition is 3099 (initially, it may look lil 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

• 6965 + 3246 + 1234 + 9847 + 8238 = ?
• Have a look at the solution below... (Click on the image to get a better view)                                 

• 1598 + 5423 + 4627 + 7953 + 8675 = ?

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Shortcut Methods for Doing Calculations

00:15 - By Unknown 0

 Decimals

Some times, you have to  convert or express the given percentages in the form of decimals. It is not such a difficult task as we think. Have a look at the following.

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

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00:14 - By Unknown 0

 Shortcuts in Division

There are so many types of divisions are there. Lets have a look.

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

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00:12 - By Unknown 0

 Shortcuts in Multiplications

NOTE : These techniques are for Mental Maths. You should do calculations in your mind only. Please avoid using Pen/Pencil and Paper. 

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

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00:11 - By Unknown 0

 Subtractions Shortcuts

PLEASE READ THE SHORTCUTS IN ADDITIONS FIRST. SO THAT IT WILL BE EASY FOR YOU TO UNDERSTAND SUBTRACTION 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

00:10 - By Unknown 0

 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

00:08 - By Unknown 0