Introduction: How to Subtract
For as long as there have been things man has taken them away from each other. This instructable is going to cover just how to subtract. Subtraction is one of the simplest mathmatical functions and is absoloutely fundamental to modern mathmatics. The first half of this instructable is going to focus on very basic subtraction for young or less able learners and in the second half will focus on some of the more complex situations (subtraction of algebraic terms and subraction of large numbers amoungst other things). Don't worry its never that hard.
Step 1: The Basics
Ok Subtraction is all about taking things away. Consider;
Mrs Brown has 5 apples sitting on a table, Mr Brown takes away2 how many are left?
We can tell this problem is a subtraction question beacuse we see the words "takes away". You may also see "minus" "reduces" or of course the word "Subtract".The first step in any subtraction is to find what the question is really asking. In the above question the usefull information is in bold. We then write this problem in mathmatical noteation "5-2". The answer to this question is three as you will be able to see in the pictures below but without actually having any apples how do we get the answer? The next steps show three basic teqniques which will boost confidence until you feel you can do subtraction in your head.
Step 2: Basic Teqnique 1
This method is a visual method designed to replicate actually having apples which is a great place to start. using the problem above you would draw five spots on a peice of paper to represent your apples. Then to subtract 2 you would draw crosses on 2 of your dots. Then its a simple case of counting those apples which are left.
Step 3: Basic Tequnique 2
This step uses two number lines. Using the apple example draw the numbers 0 to 5 left to right on your page. Then do the same from right to left on yor page (prefrablly in a different colour). Then find the number you are subtracting on one of your lines and the number on the other line that coressponds to it is your awnswer.
Step 4: Basic Teqnique 3
The last two techniques have worked well for our apples example but are relatively slow and do not work where an answer that is a negative number arises. This technique, while still simple to do, is the next step to doing simple subtraction in your head and can cope with more complex examples.
For this technique we will do 10-14
Raise as many fingers as the number you are subtracting from, in this case 10. Now count to 14 each time lowering a finger. When you have no fingers left , make a mental note and start raising them again until you have finished counting to 14. In our example you will have gone to 0 fingers and now have 4 fingers raised. Because you went to zero fingers the fingers still up represent negative numbers. This is no drama just be sure to put a subtract sign in front of the number four as your answer. If you never go to zero fingers the answer will be a regular positive number. If you can tell straight off that 14 >10 (14 is greater than 10) and therefore that the answer will be a negative number just count up from ten to 14 raising a finger each time (rember that answers will be negative). This technique only works for numbers being subtracted from below 10 and answers above negative 10 but once mastered will make more difficult steps later in the Instructable easier.
Step 5: Pen and Paper Method
This method is getting a little more grown up and a little more useful for everyday things. First write the number you want to subtract from then underneath the number you are subtracting. Start with the "ones" (least significant number) subtract the top from the bottom, this subtraction should be simple enough to do in your head if not use one of the above methods. Then move on to the next column and continue left along you numbers you are subtracting from. Write the results of your mental calculations below the numbers used in the calculation as you work them out. The number you should now have at the bottom of the columns is the result of the calculation.
If the number you are subtracting in a particular column is larger than the one being subtracted from, reduce the number to the left of the number being subtracted from by 1, and add that 1, as 10, to the number being subtracted from then continue to subtract the number being subtracted (quite a scentence I know but it should be clear in the example below).This is called borrowing. This method meas you only have to know how to subract numbers below 20 and you can subtract enourmous numbers from one another. To briefley explain the below example 4-6 gives a negative result so we "borrow" a ten from the 30 to the left of the 4 reducing the 3 to a 2. 14-6 is 8 so we write 8 bellow the 4-6 column then we do 2-2=0 and write that below that column. The number at the bottom is then 08 and sure enough thts the right answer.
Step 6: Algerbraic Subtraction
When we use letters inststead of numbers when subtracting there are a few things to consider:
x-x= 0 Any term subtract itself is zero
x-y =bleurgg You cannot subtract two different terms from one another. You can't take two pears from three apples
xy-y does not =x let y be 4 and x be 3 12-4 is not the same as 3
x-x does not =x either
2x-x = x When terms are all the same just ignore the "x"s until the end and then when giving your answer stick an x after it. If there is no number in front of a term it is a 1 (in this case 2-1=1)
Step 7: Further Subtracting
Now go forth and ...Subtract? Yes subtracting doesnt finish here check out others instructables on how to subtract fractions.Want to subtract decimals? Just view the decimal to fraction instructable first. There are seriously millions of applications for subtraction (in fact infinate applications) but millions of useful applications. Just go and see how usefull it is. If subtraction becomes a big part of your life get a calculator! The methods above are all great but sometimes it's nice to get the last bit of helpfulness out of a machine before they rebell. If you were deeply moved by this instructable your a bit wierd but I love good comments!