2.4+Subtracting+Integers

Section 2.4 - Subtracting Integers
(After Spring semester, combine this section with the previous one!)


 * Turn it into Addition**

If you "add the opposite" of a number, it is the same thing as subtracting. This is conceptually challenging for many people. Someone should figure out how to explain it better and post it here.

7 - 5 = 2 7 + ( - 5 ) = 2

You can turn any subtraction problem into an addition problem just by changing it so that you are adding the opposite. Just like the example above.

However, it kind of messes up the vector method of adding integers, so let's modify that a bit. Let's say that if you encounter a negative sign in a problem, you switch the direction of the vector from the direction it was going. We assume we are always headed in the positive direction to start with.



So, the green arrow represents the problem ( - 2) + 3 = 1. The red arrow represents 8 - 3 = 5. But let's say you were moving through that last problem and then came upon the minus sign and said to yourself, "Hey, that means go in the other direction." Rewriting the problem as an addition problem, we get 8 + ( - 3 ) = 5. Start with 8 and you are going to add, but then all of a sudden you see the minus sign and go in the other direction and subtract.


 * Subtracting a Negative Number**

If you follow that same logic, what would happen in this problem: 5 - ( - 3) ?

Start on the numberline with 5, then go left to subtract, but then you see another minus sign and switch directions and you really end up adding 5 and 3 to get positive 8.

There is a way to explain this idea with IOUs in a poker game, but it is still hard to understand for many people. If you subtract an opposite, it is like adding. Kind of like a "double negative" for you English majors as well.

The simplest rule is, ** if you see two minus signs right together, just turn them both into a plus sign and add. ** This works every time, but only if the minus signs are right next to each other (parentheses does not split up minus signs in this case).

6 - ( - 3 ) is the same thing as 6 + 3.

But, - 6 - 3 is not the same thing. It is the same as - 6 + ( - 3) = - 9. (Start at negative six and subtract (add an opposite) three to get to minus nine.)

If you turn all subtraction problems into addition problems, you can use the same two rules for adding integers:
 * If the integers have the same sign, add their absolute values and use the common sign. **
 * If the integers have different signs, subtract the smaller absolute value from the larger, but use the sign of the larger. **


 * Practice Problems for Adding and Subtracting Integers**

**Where to from here?**
2.1 Integers 2.2 Absolute Value 2.3 Adding Integers 2.4 Subtracting Integers 2.5 Multiplying Integers 2.6 Dividing Integers 2.7 Exponents and Roots Chapter Two Summary Chapter Two Homework