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March 26th, 2017, 10:42 AM   #1
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easy way to subtract large numbers

Hi,

I am looking for an easy way to subtract large numbers without the use of a calculator.

Numbers such as:

717299874, 238303931, 279890276, 215879628, 359239774, 825753868, 928942504

Any tips?

Thanks,

Neta.
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March 26th, 2017, 11:06 AM   #2
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Quote:
Originally Posted by neta12 View Post
I am looking for an easy way to subtract large numbers without the use of a calculator. Numbers such as:

717299874, 238303931, 279890276, 215879628, 359239774, 825753868, 928942504
Why?
Subtract from what?
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March 26th, 2017, 01:49 PM   #3
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It may be tedious, but elementary school method works fine.
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March 29th, 2017, 10:31 AM   #4
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When I was in early elementary school I had difficulties with "the borrowing method" of subtraction. I especially found it confusing if there were a lot of zeros in the minuend.

Then in grade 5, I was taught that instead of "borrowing" you could add 10 to both the minuend and the subtrahend.

Example:

83
46

1. First add 10 to 3 in the minuend to make 13 (just as you would do with the "borrowing" method.
2. then add 10 to the 4 in the subtrahend, so that is becomes 5 tens instead of 4 tens.

Subtract 6 from 13 and get 7. Then subtract 5 from 8 to get 3. So the answer is 37.

This works fine no matter how large the minuend and the subtrahend. I still use this technique to this day.

Last edited by Timios; March 29th, 2017 at 10:35 AM.
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March 30th, 2017, 08:50 AM   #5
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Quote:
Originally Posted by neta12 View Post
Hi,

I am looking for an easy way to subtract large numbers without the use of a calculator.

Numbers such as:

717299874, 238303931, 279890276, 215879628, 359239774, 825753868, 928942504

Any tips?

Thanks,

Neta.
As MathMan said, elementary subtraction is fine. I'd recommend that to anyone.

However, there's a nice mental method for subtraction, outlined below. It is similar in spirit to what Timios posted.

Important note... anyone using this method should be comfortable with subtracting using the standard elementary methods first; it does not replace it!

Just as an example, I'll consider some smaller numbers...

Consider:

Code:
 7172
-2380
  -----

  -----
Follow these instructions:
1. Go left to right -->
2. For a given position:
a) Work out what you need to add to the bottom number to make the top number and think of it (e.g. '5')
b) take a glance at the next cell to the right. If the lower number is greater than the top number, take one off your number (3 > 1, so my number is now '4')
c) say the number out loud or write it down
3. remember that if you subtract one in part c), make sure that when you go to the next position you need to add to make up 10 + digit, not just the digit.
4. go to 2 a).


The literal numbers I'm thinking of during the process are '5', '4', '8', '7', '9', '2' with the ones in bold being the ones I say or write down as I'm going through the mental method.

So following those steps I obtained the answer as '4792'. I worked it out by doing in my head, but it took me maybe 10-12 seconds or so because I haven't practiced it much. With practice you can do it very quickly and for large numbers too.

Note that if you're saying the digits, your answer will be read out as "four, seven, nine, two" rather than "four thousand, seven hundred and ninety two".
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March 30th, 2017, 09:02 AM   #6
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7172
-2380

Subtract 2400 : 4772

Add 20: 4792

Ahem!
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March 30th, 2017, 02:53 PM   #7
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If you find it easier to add than subtract, then you can convert the subtrahend to its tens complement. Using the example of 7172-2380:

Code:
 7172
-2380

You convert 2380 to its tens complement by subtracting each digit from 9 (yes you still have some simple subtractions, but there are no borrows) and then adding one.
The tens complement is:

Code:
 9999
-2380
–––––
 7619
    +1
–––––
 7620
which you can do in your head as fast as you can write the number down.
So the tens complement of 2380 is 7620.

Now just add 7172+7620 and lop off the most significant digit:

Code:
  7172
+7620
–––––
14792
Minus the first digit gives the correct answer 4792.
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April 18th, 2017, 03:34 PM   #8
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It's a great method, Yooklid!

But I think you means the NINES complement.
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April 19th, 2017, 11:47 PM   #9
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No. Nines complement is what you get by subtracting each digit from nine, but when you add one to that result you get the tens complement.
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April 25th, 2017, 05:05 PM   #10
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So when you say "the tens complement" you are referring to the final digit only?
For all the other digits, it is the nines complement.

In any case, I am fascinated with the technique! I have never encountered it before.
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