This post is continuation of learning integers series and it is the second post after introduction to integers. In this presentation we will explore adding integers and wipe out many misconceptions about number addition facts.
Integers are positive and negative numbers (except zero, which is the neutral integer). Remember, every integer has its sign (Positive or negative) at its left front. Also remember that, most of the times positive sign is not shown in front of the positive integer. For example, 1 is +1, 2 is +2 and 3 is +3 and so on for rest of the positive integers.
Again, all integers have their sign (positive or negative) at their left front and if there is no sign at the left front of an integer that means the integer got plus sign which is hidden and need not to be shown.
Let's explore further and learn a trick to add integers: Remember: "Same signs add and keep, ADD and KEEP."
If two or more integers have the SAME SIGNS, ADD THEM. Keep their common sign in front of the answer that you just got by adding the numbers.
For example, you are already doing the following since you were in grade 2, but today you will learn this from a different point of view or from an integer's point of view:
Simplify the following:
1+2 = ? Easy, isn't it 1 + 2 equals 3 so we write it as 1 + 2 = 3
You might be wondering that, you already knew this. What's new? The answer is, yes! You already know that 1+2 equals 3. My goal here is not to teach you "whole numbers' additions" but the integer's additions.
For this long, you are dealing with the whole numbers and natural numbers, but today you will learn how 1+2 is done, considering them integers (as all the whole numbers are integers).
So, here is the solution: For now on, whenever you are adding or subtracting the numbers, consider that you are dealing with integers and .......integers are the signed numbers.
Look at the above question, 1 got the plus sign at its front (the sign is not not shown, but it is understood that, "+" sign is at its left front). Also, 2 is positive as it has "+" sign in front of it.
This is very important to note that the "+" sign in front of 2 belongs only and only to 2 and it has nothing to do with 1 (as most of students consider that the sign at the middle of two numbers is common to both the numbers). "1" got its own plus sign at its left front which is not shown and understood or very common in mathematics.
So, in our question, 1 got plus sign and 2 got plus sign, which means both numbers got the same signs.
"Same signs add and keep, ADD and KEEP."
Therefore, we add 1 and 2 to get 3, actually +3 (keep the common sign with the answer which is plus). But, positive sign at front of a leading integer need not be shown, so you can leave the answer as 3 instead of +3.
Now simplify: - 1 - 2 =?
Probably, you have understood the above question now. Always look at the signs of integers at their left front, and in this question both number have the same signs (which are negatives). Again, our rule for same signs applies, numbers got the same signs, so add them to get 3 and answer will take the common sign which is negative.
Therefore, the answer for above example, - 1 - 2 is equal to -3. Remember, we can't leave the answer as 3 here (which means +3 but the answer is -3), because in case of a negative sign we have to show it and it is never ever hidden like a plus sign.
Below are some more examples:
Hope that above presentation will clear out the misconception about adding integers for grade 6 and higher level students. In our next presentation we will explore the rule to subtract the numbers.
Meanwhile "God Bless us ALL"
