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Section 1.4: Adding and Subtracting Real Numbers Worksheet 1.4

Any real number can marry any other real number. So if a real number is in love with itself, it can still get married! Indeed, the number world is truly mad!

Last time we talked about positive numbers. Now we look at all real numbers. This includes every positive's cantankerous, pessimistic, negative twin. We also have that number we love so well...









Some Ground Rules: when the negatives show up, we need to establish some rules of civility.

Rule #1: Subtraction is the addition of opposites. That is, you can always turn a divorce into a marriage. How, you ask, can we do that?! $$a-b=a+(-b)$$

Example: $3.15-(-5.86)$.













Rule #2: Addition is associative. That is, marriages can be performed in any order. $$a+b+c=(a+b)+c=a+(b+c)$$ Example: $3.15-(-5.86)-\frac{1}{2}$.











Rule #3: Addition is commutative. That is, if $a$ marries $b$, or $b$ marries $a$, the result is the same. Duh!!! $$a+b=b+a$$

Example: $3.15+(-5.86)$ is the same as $-5.86+3.15$.

Real World Application: You use the commutative law almost every day. How can that be?! D:











Rule #4: Do what's in grouping symbols first.

Example: $[-5 + (-6) + (-7)] + [8 + 4 + 3]$











Application: Use this bar graph to determine the change in net income for Ford Motor Company
  1. from 2005 to 2006
  2. from 2006 to 2007