Mathematics

How to Add and Subtract Integers



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Integers are whole numbers that run from negative infinity to positive infinity, including 0.  Adding and subtracting integers is a basic component of math, and this article will explain how to do so.

>>> Adding Integers <<<

The process of adding integers can be applied to a number line.  Here is an example of a number line that you could use for this:

to negative infinity  <-(-4)-(-3)-(-2)-(-1)-0-1-2-3-4->  to positive infinity

If you look at the equation 5 + 3, then you would be at positive 5 on the number line, then you would add positive 3 (which would make you go to the right on the number line), leaving you with positive 8.  This same idea applies to adding negative numbers as well.  Take the simple equation 6 + (-3).  You would start at positive 6 on the number line, and then when you add negative three, you would move three units to the left (towards zero and the negative side), leaving you with positive 3.  As another example, (-4) + (-8) would be negative 12 because you would start at (-4) and move left 8 units which would bring you to (-12).

>>> Subtracting Integers <<<

When subtracting integers, remember this one simple rule: "Add the opposite of the second term".  The "second term" means the second number, or the number that is being taken away from the original number by subtraction.  To explain what this means, let's take a look at an example.  To "add the opposite" in the equation 4 - 7 would mean that the equation would become 4 + (-7), which equals negative 3.  Both equations yield the same answer.  By "adding the opposite" (of the second term), you can use your previously learned number line method.  Still adding the opposite, (-7) - (-8) would become (-7) + (8) and would equal positive 1.  I hope this makes sense, because remember, if you "add the opposite", then you can use the number line method.

Now that you know how to add and subtract integers, try these example problems.  Although these problems may not seem too difficult, they will test your knowledge of the concepts regarding adding and subtracting integers.  The answers can be found at the end of this article.

1.)  12 + (-5) = ?

2.)  (-9) + (-20) = ?

3.)  18 + 13 = ?

4.)  (-33) + 29 = ?

5.) 17 + (-25) = ?

6.) 45 - 24 = ?

7.) (-9) - 17 =?

8.) (-20) - 4 = ?

9.) (-2) - (-14) = ?

10.) 21 - 38 = ?

Answers: 1.) ?  = 7, 2.) ? = -29, 3.) ? = 31, 4.) ? = -4, 5.) ? = -8, 6.) ? = 21, 7.) ? = -26, 8.) ? = -24, 9.) ? = 12, 10.) ? = -17

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