Introduction: 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.
Step 1: 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 , 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
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).
Step 3: Subtract – the American Method
The way most North American students are taught to solve this problem is to think something like this:
Take away  from  - Oh wait, you can't because  is less than  so we need to borrow 1 from the tens column, and remember that for later - now take away  from 15 which leaves 7 - Ok, then take  away from  - I mean 8, because we borrowed the 1 from the tens column, remember - So then take away  from 8 to leave 6 - The answer should be 67 - Right??.
Sound familiar, sure it does. Talk about a confusion of thinking with some error prone parts to mess up, like the borrowing and remembering you borrowed etc, Plus the difficulty of learning the concept. It is a wonder any of us managed to program out minds to think like that.
Step 4: Don’t Subtract Add – the Austrian Method
Try to follow the Austrian or Additions Method thought process of the same example.
What do you need to add to  to equal 15 (because  is bigger than  we make it 15, answer is 7 - now only because we made  be 15, add 1 to the  giving you 3 - now what do you need to add to 3 to get , that would be 6 - so the answer is definitely 67.
Notice the elimination of borrowing from the tens column to remember, and instead carry over and add the 1 to the subtrahend digit in the next column. The carrying is easier than borrowing and remembering. This simple idea clears the most common error in subtracting.
Important to note the Addition Method is so simple that Europeans are taught this method solve difficult multi-digit subtractions in their head.
Step 5: Proof It to Yourself
If you are one of those, like me, who need to see it to believe it. Try this test.
Without aid of pencil and paper - Do this equation both ways.
Hint, you need to have the same answer!
Step 6: Test Answers
Of course it was easier to use the Austrian Method. Were you even able to do the American Method in your head?
Test your friends. Challange them to see who can subtract large numbers in their head.
Did you get 17268 as the answer??
Step 7: Subtracting a Bigger Number From a Smaller
Oh, one last point of interest is when you need to subtract a larger number from a smaller one.
Using either Method, make the larger number the minuend and the smaller one the subtrahend proceed as you would to solve for the difference and then just place a "-" sign in front of your answer. How neat is that.
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