2.3+Adding+Integers

Section 2.3 - Adding Integers

 * Parentheses around Numbers**

Often, particularly when working with negative numbers, you will find numbers written within parentheses, for no apparent reason. The reason is sometimes just to keep the numbers separate, or perhaps to separate operations, such as two minus signs right next to each other.

6 - 2 is the same thing as (6) - (2)

Although it isn't very important with positive numbers, it is a good idea to put negative numbers parentheses because they tend to get more confusing, particularly in this section and the next.


 * Vectors on the Numberline**

In case you didn't watch //Despicable Me//, or pay close attention to the introduction of the character named Vector, ** a vector is like an arrow that has a direction and a magnitude **. Although it can be more complex than that, it is pretty easy to use a vector to add or subtract integers. Think of a vector as an arrow going either right (positive) or left (negative) and being a certain number of spaces long. An arrow that is five spaces long and pointing right would represent positive five, or adding five. Likewise, an arrow that is three spaces long, but pointing to the left, would represent subtracting three.



It doesn't matter if the arrow starts at zero, or below zero, or in the positives -- the direction of the arrow (vector) indicates whether you add or subtract, and the length of the arrow shows how many to add or subtract.

Use the numberline above to see how this works for a few different addition problems. Start where the first number is on the numberline, then move to the right (add) or left (subtract) the same number of spaces as the second number.

6 + 3 = 9 7 - 3 = 4 2 - 9 = -7 ( - 4 ) + 3 = - 1 ( - 3) - 5 = - 8


 * An Alternative Rule for Adding Integers**

This is a different way to think of adding integers that doesn't use the vectors. If you are more of a "rule" type thinker than a visual one, this might help. It always works!

There are two rules for adding integers:
 * If the integers have the same sign, add their absolute values and use the common sign. ** 4 + 3 = 7, just like regular addition ( - 4 ) + ( - 3) = - 7, add the 4 and 3 to get 7, but use a minus sign because that is the sign they both have.
 * If the integers have different signs, subtract the smaller absolute value from the larger, but use the sign of the larger. ** 6 + ( - 2 ) = 4, 6 is larger, so 6 - 2 is four and because the larger number was positive, the answer is positive. ( - 9 ) + 2 = - 7, Nine is bigger (absolute value), so 9 - 2 is 7 and because the larger number was negative to begin with, the answer is - 7.

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**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