Instructables
Picture of How To Subtract

Subraction is the next logical extension of addition and yet causes confusion in students both young and old. Why? We were taught to solve subtraction problems in a confusing way.

I am going to show you a very simple way to subtract large (multi-digit) numbers. You will wonder why they never taught this method in school.

First we need to set some reference points so you can follow along with the concept.
 
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Step 1: Subtraction, Why the Confusion?

Picture of Subtraction, Why the Confusion?

Subtraction, Why the Confusion

First - Forget what you were taught, subtraction is really a myth. Addition is where it is at.

Next - I am going to assume you already know a little bit about basic arithmatic, because you are already on the Internet and so can read. I will also assume you know what happens when you had 5 pennies and you lost 2 of those pennies.

KISS, Keep It Simple Silly and don't make subtraction hard on youself.

Each example uses only one of each digit, so you will know exactly which digit is referred to.

In text, each digit from an example will be referred to within square brackets [0], other numbers will be without them.

Terms such as minuend (a) - subtrahend (b) = difference (c) are odd words used to identify and denote parts of the subtraction. Now I do not care if you call them 'one' number, without 'the next' number leaves the "answer'. Just that we both know which is which when I mention them.

Step 2: Review Of Some Basics

Picture of Review Of Some Basics

According to Wikipedia - Subtraction is one of the four basic arithmetic operations; it is the inverse of addition, meaning that if we start with any number and add any number and then subtract the same number we added, we return to the number we started with. Wow! Now that that is clear.

In mathematical expression, subtraction is denoted by a minus sign in infix notation (a complicated way of saying equation all written on one line). Hmmm, not much better.

The traditional names for the parts of the formula

a - b = c

Where the minuend (a) - subtrahend (b) = difference (c).

cute kitty2 years ago
this is aaaaaaawwwwwwwweeeeeeesssssssooooooommmmmmmeeeeeee it saved my life if there was not this thing i would die by my teacher!!!!!!!!!!!!!!!!!!!!!!!!!!
Everyone out. I have to poop. This is amazing. Why were we not taught this method?
arcticpenguin (author)  mwassenhoven3 years ago
Mostly because of a conspiracy from teachers to stretch the little we need to learn into decades of boring classrooms. LOL
North American teaching methods believe the system they taught us is far superior to this European technique. Like-wise with whole word language learning. Don't get me started. LOL

arcticpenguin (author) 3 years ago
ouch, small typo, um that 29,500 should read 28,500
sharpie333 years ago
okay can you help me with subracting 30,000-1,500 i keep getting 38,500 how do you get the 2 in instead of 3. so when you subtract it is left to right or still right to left??
arcticpenguin (author)  sharpie333 years ago
Sure, I can help. (without rereading my instructable, sorta like one hand behind my back.LOL)

Your example has 6 zeros and the answer has a few too, so it can get real messy real fast describing it, so I'll do each thought process step by step. You will get the aha! moment along the way.

30,000
- 1,500
| | | | |__ think "0 plus 0 gives 0"
| | | |_____ think "0 plus 0 gives 0"
| | |________think "5 plus 5 gives 10" carry forward the 1
| |___________think "1 plus the carried 1 plus 8 gives 10" carry forward the 1
|______________think "the carried 1 plus 2 gives 3"

= 29,500

Working right to left.

It becomes a much more valuable technique the more different the digits are. With so many zero's it is easier to do it other ways, I'll admit.

Now try it with 34,567 - 8,629 and it becomes just as simple as the above.
it quickly becomes

9 + (8) is 17
1 + 2 + (3) is 6
6 + (9) is 15
1 + 8 + (5) is 14
1+(2) is 3

* in the brackets are the answer digits right to left, all the 1's (in this example) are due to carrying forward.

Oh, yeah the answer is 25,938 and with practice can easily be done as quick as you could read it. And it never gets more difficult even when the numbers are larger.

If you do have the aha! moment..... go try subtracting your phone number from your friends, forget about the dashes; and to avoid identical area code thing (yeah use all 10 digits) write one of the numbers in reverse; and you may as well use the higher first digit as the top number.

Rhamza4 years ago
Wow, thank you so much for posting this. it is remarkably easy to subtract without paper now. much much better! Thanks!
 
scurtindale4 years ago
Amazing! This is so awesome. I tried it and it works so easily and without any effort. I tried to do some really long problems and i didnt even need to write. Thanks. Im gonna forget the American way! LOL
Could you please explain to me how I would subtract 2000.00-632.84? I keep coming up with the wrong number. Your help would really be appreciated. Thanks :0)
arcticpenguin (author)  porcupinemamma5 years ago
Sorry for the late reply. Just found your question. 2000.00 -632.84 Always work from right to left..... 4 and 6 makes 10 6 is the right most digit. add the 1 of that ten to bring the 8 to be a 9 9 and 1 makes the next 10 1 is the second from right digit keep the decimals point lined up. add the 1 of that ten to bring the 2 to be a 3 3 and 7 makes the next 10 7 is the third from right digit add the 1 of that ten to bring the 3 to be a 4 4 and 6 makes the next 10 6 is the fourth from right digit add the 1 of ten to bring the 6 to be a 7 7 and 3 makes the next 10 3 is the fifth from right digit add the 1 of ten to bring the 0 to be a 1 1 and 1 makes the 2 1 is the sixth from right digit You're answer should then be 1367.16 While it seems awkward at first, after a few tries you'll see it is just as easy as addition. If you are still having difficulty try email egon-1@rogers.com and I have other ways to teach this. What part of Ontario? Hope that helps;)