How to Subtract Numbers Mentally at Super Fast Speed.

Mental subtraction strategy for any size number.How to subtract numbers mentally fast.

 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 the same number to both A & B and the value of expression will not change. Similarly you can subtract too the same number.

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.

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Niraj Tulsyan

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