In this article, you are going to learn subtraction strategy for mental subtraction of small or large numbers at super fast speed.Average time to read the article is less than 5 minutes.

Without wasting time let us take first example.Here we will subtract small numbers.Later on, the same process will be applied to large numbers.

1st Mental subtraction strategy:

Lets start with small numbers.
45-33=?

45 consists of 40 and 5,
33 consists of 30 and 3

40-30=10
5-3=2
Now add 10 and 2=12

Take some other subtraction examples:

Example: 83-22=?

80-20=60
3-2=1
60+1=61

Example: 87-68=?

80-60=20
7-8= -1

20-1=19

Now move on to subtraction of larger numbers

Example 1:

  • 5678-34=?
  • 56 won’t be affected 78-34= 70-30+8-4=40+4=44
  • Result=5644

Notice that to subtract we convert the numbers into 10’s multiple.It is easy to think in terms of 10’s multiple.

Like if you have 5678 think it as 5 000, 6 00, 70 , 8. We subtract only corresponding  10’s multiple.

Example 2: Solve this tricky one:

  • 5623-34=?
  • 34-23=30-20+4-3=11
  • 5623-34=5600+23-23-11=5600-11=5589.
  • Think it as , since 34 is 11 greater than 23 we will subtract 11 from 5600.

5623=5000+600+20+3

34=30+4

20-30=-10

3-4= -1

total value =-11

net result 5000+600-11=5589

2nd subtraction strategy:

In this process we try to manipulate numbers to nearby numbers.

First take small numbers.

43-37, to do this apply my golden rule.

Golden Rule 1 for subtraction:

In an expression of the form A-B , you can add or subtract the same number to both A & B and the value of the expression will not change.

Like in 43-37, add 3 to 37 so that it will become 40, add 3 to 43 this will become 46,

Now 46-40=6

Some more examples on this,

68-23=70-25=45, added 2 to each one.

76-34=72-30=42, subtracted 4 from each.

413-205=408-200=208, subtracted 5 from each one.

Golden Rule 2 for subtraction

These is based on manipulating both A & B  in an expression A-B to nearby integer values .And compensating the result in last.

Example:

87-28

90-30=60

3-2=1, manipulation of plus 1  means we get 1 more than actual value. So to compensate we subtract 1 , hence the net result= 59

Obviously you can do it also as 80-20 +7-8=60-1=59

Now move onto some tough subtractions

Let us take  Example:

  • 14,6794 – 3457=?
  • 14 will not be affected think on 6794 and 3457.
  • 6794=6800-6 –> here you can see I have manipulated 6794 to nearby number 6800

3457=3460-3 —> manipulated to nearby number 3460

  • 6800-6-3460+3=6000-3000+800-460-6+3= 3000+800-500+40-3=3000+340-3=3337 , notice that 460 is manipulated to 500-40
  • So, result will be 143337
  • You can think it as addition of 6 in 6794 and 3 in 3457. So, net result must be (6-3=3) more than actual value . Hence, we will subtract 3 in the last to compensate.

In this second subtraction strategy you can notice that I have also used the first subtraction strategy.

Now as you know the  subtraction strategy we will move to larger numbers.Try to solve the below example mentally.

Learnt mental subtraction strategy, solve My challenge:

Example:

  • 18,75674-5820
  • 18 won’t be affected, 75674-5820= 75674-5674-146=70000-146=70,000-150+4=69854.Therefore, result  is 18,69854
  • Used in above 5820-5674=5800+20-5600-20-54=200-54=200-50-4=150-4=146
  • 75674= 70,000 +5674 , Base value= 70,000. I first see it as 74 and 20 has diff of 54(+ will be added to base value)

And 5800 and 5600 has diff of 200(- will be subtracted from base value as 5800 is greater than 5600). So ,net 200-54=146 will be subtracted from base value.

  • 5820 – 5674 , 200-54=146

You may be wondering is this mental math at all?. Possibly  you are still thinking with pen & paper and not with your mind alone.I have broken the process into steps  we process in our mind.

Try to picture in terms of words rather than numbers while performing mental calculation.

Example:

  • 123, 45789-14367
  • 123 won’t change, focus on 45789-14367
  • 45789= forty five thousand +seven hundred+89
  • 14367= fourteen thousand+ three hundred and 67
  • Forty five thousand – fourteen thousand= (45-14) thousand=31 thousands
  • Seven hundred – three hundred= four hundred
  • 89-67=80-60+9-7=20+2=22
  • So, result will be 31 thousands, 4 hundreds and 22
  • Hence net result= 12331422

Suppose if you are given this tricky example below.Can you find what is tricky here?

Example:

  • 45312-14837
  • 45 thousand three hundred and 12 – 14 thousand 8 hundred and 37
  • 45-14=40-10+5-4=31 thousands.
  • 300-800=(-)500 will be subtracted from net result as 800 is greater than 500.
  • 12-37=(-)25 will be subtracted from net result.
  • 31000- 500-25=30 thousand plus ten hundred – five hundred – 25=30 thousand plus five hundred -25=30000+4 hundred +1 hundred-25=30000+4 hundred+75=30,475

You can think as follows:

Calculating 45312-14837.

To calculate in mind you need to first subtract 45-14=31

Then as 837 > 312 subtracting will give 525 which must be subtracted from 31000

1000=525+475 (you can visualize it easily), So we immediately can write 31000-525=30000+475+525-525=30000+475=30475.

You won’t be benefited in terms of speed if you don’t practice it mentally . Try to practice as much as possible to make it natural to you.

So, by manipulating numbers to nearby easier numbers you can calculate difference easily. Also try to think in terms of words or money while subtracting.Like if you subtract 567-139 ,think it as $567- $139=($500-$100 , $67-$39) =($400 , $28)= $428

67- 39 can be done by manipulating as 70-40=30, as 3 added to 67, 1 added to 39 = 3-1=2 added , so to compensate we subtract 2 from 30 so the result will be 28.

Okay! Now can you apply your newly learnt mental subtraction strategy ? Try to solve these examples in your head as fast as possible.

Examples: 17-68 , 95+44,33-11, 106-67, 784-238, 4356-478,  15671-9812 , 122+564-234 , 98456-34562 , 124689-57389 , 4528950-489100+34357 etc.

Hope you enjoyed the article.Thanks.Do not forget to share.You can also read Mental Addition Trick-Learn within 5 minutes.


Niraj Tulsyan
Niraj Tulsyan

Btech in Electronics & Communication.I love Maths, Science & Technology.

    11 replies to "How to Subtract Numbers Mentally at Super Fast Speed."

    • […] We will explain this process in more details in  How to subtract numbers mentally at super fast speed. […]

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    • Leyla

      Thank you can you please do the same tricks in decimals I.e. 9.30-8.20

    • sangammal

      Sir I need simple and easy multiplication and division methods

    • little samal

      ohhh great trick ,it will help me for bank exam

    • Nitin Mishra

      Thanks..

    • Princeton University

      It’s surprising to find on mathsequation.com a resource
      so precious about equations.
      We will note your page as a benchmark for How to Subtract Numbers Mentally-at Super Fast Speed.
      We also invite you to link and other web resources
      for equations like https://en.wikipedia.org/wiki/Equation.
      Thank you and good luck!

    • chumendra bhagat nagwanshi

      thanks bro

    • Gokul krish

      Sorry this is already exist in vedic mathematics

      • Niraj Tulsyan

        Sorry, bro then you have not read Vedic maths at all. The process and approach to subtract numbers I explained is very different from one explained in Vedic Maths.My method is more focused on how well you can remember the intermediate calculations if you think in terms of multiples of 10 and then subtract. While in Vedic Maths you subtract thinking of 1 digit of each number at a time.While in my method it’s possible that you can think of more than one digit while subtracting. For example, 43340- 1247, in this example from my method it will be like 43 thousand-1 thousand=42 thousand, 300-200=100,mentally update 42thousand as 42 thousand 100, 40-47=-7, mentally update 42 thousand 100 to 42 thousand 93, 42093, As you can see many times I have worked on more than 1 digit also it’s easy to work completely in mind this way as you can easily remember the intermediate calculation because we update our previous intermediate calculation in each new step.So basically there will always be only one intermediate calculation you will need to remember.While in Vedic method you will think digit by digit so you will write first 4, then 3-1=2, then 3-2=1, then 4-4=0, then 0-7= 7 bar, 42107bar, answer will be 42100-7=42093, 43340-1247, in this approach you work digit by digit and in the last you adjust the bar digits from the number.It’s not easy to calculate everything in mind this way as you’ll have to remember those intermediate steps.Also, it will become more difficult to remember intermediate calculations in vedic method with a larger number.I hope this explanation will be helpful for you.Thanks

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