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By looking at the patterns in the results of the various operations, we can further summarise them as well as simplify them. The final results are given below.
Addition & Subtraction
Again by looking at the pattern, we can simplify the rules as follows.
When either of the operators occur in pairs (++ or --) the result is “+”.
It can also be stated in a different form
The + operator does not change the sign which comes with it.
The - operator inverts the sign which comes with it.
A Subtle Difference
The above rules work in different ways – one for addition & subtraction and the other for multiplication & division. This is an important difference which needs to be understood.
In multiplication & division, these rules give us the sign of the “product. For example, -4 X -3 = +12 and -4 X +3 = -12.
In addition & subtraction, these rules convert an integer operation into a simpler & familiar whole number operation. For example, -4 + (-3) becomes -4 -3 which is -7. Also -4 – (-3) becomes -4 +3 which is -1.
Multiplication & Division
We see that the rule for multiplication & division are very similar as in the case of addition & subtraction, if we ignore the multiplication sign coming between the - & + signs.
Negative X Negative = Positive
Out of all the operations, the one that makes students most uncomfortable (hence the teachers too!) is that in multiplication, negative X negative = positive. This seems to go completely against common sense. But we can find examples of this in our daily language!
Take 2 sentences (a) Ram is a tall boy & (b) I am NOT saying that Ram is NOT a tall boy. Both sentences convey the same meaning. In the second sentence the two negatives taken together mean the same as the first sentence.
It is NOT correct that you need NOT wear a mask! - means that you need to wear a mask.
Poet W H Auden has expressed his impatience with this rule in the following 2 line poem.
Minus times minus is plus,
The reason for this we need not discuss
Uniformity in Integer Operations
We see that in all the 4 operations, the rules governing the results when the 2 operators combine seem very similar. This makes them easy to remember.
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