1.03  Signed Numbers; Absolute Value

Basic Algebra: One Step at a Time.  Page 13 - 20:   #107, 109, 110, 111, 114, 115, 116, 117, 118.

Dr. Robert J. Rapalje

Seminole State College of Florida

Sanford, FL  32773  

To see Section 1.03, with detailed explanations, examples, exercises, and answers, click here!

107.                   

            Well, that’s what it looks like in black and white.  Let’s color it up a bit.

Remember that  and    

109.                  

Remember that  and    

                              

110.                   

            Here it is in color.

Remember that  and    

111.                   

            Well, that’s what it looks like in black and white.  Here it is in color.

Absolute value symbols are considered to be symbols of grouping, so they are treated as parentheses within the order of operations.  In other words, you have to do what is within the absolute value bars first, as if they were parentheses.

                                   

114.                   

            In color perhaps it might look like this:

The first step is to combine the numbers inside each absolute value, as if these had been parentheses: 

115.                   

            Colorizing it, it might look like this:

As before, the first step is to combine the numbers inside each absolute value.

116.                   

            In color perhaps it should look like this:

Notice that when I “colorized” the problem above, I deliberately did NOT color the negative before the 8 to match the .  It is very important to know that, since there were no parentheses around the -8, the only thing that gets squared is the 8!  The negative before the 8 is NOT squared!

117.                   

            In color perhaps it should look like this:

This is exactly the same as #116, except that it is a subtraction instead of an addition problem.  You can finish that one yourself, right??

118.                   

            In color perhaps it should look like this:

Notice that when I “colorized” the problem above, I deliberately did NOT color the negatives before the 5 and the 3 to match the 5 and the 3.  It is very important to know that, since there were no parentheses around these negatives, these negatives are NOT to be squared!

                                

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