Math
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Dr.Peterson
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Please tell us your thinking, so we can tell what sort of help you need.
I'm a little confused, because I don't see a number line; but I think you are supposed to evaluate each expression and then put them in order. What values do you get?
HallsofIvy
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The problem asks you to do the arithmetic.
The first is \(\displaystyle -3\frac{1}{2}- (-5)\). Do you understand that -(-5)= 5? Do you see that \(\displaystyle -3\frac{1}{2}+ 5\) is the same as 5 minus \(\displaystyle 3\frac{1}{2}\)? Do you understand that \(\displaystyle 5= 4\frac{2}{2}\)? Can you do \(\displaystyle 4\frac{2}{2}- 3\frac{1}{2}\)? Or (a different way of doing the same subtraction) \(\displaystyle \frac{10}{2}- \frac{7}{2}\)? Do you see where \(\displaystyle \frac{10}{2}\) and \(\displaystyle \frac{7}{2}\) came from?
The second problem is \(\displaystyle -3\frac{1}{2}-3\frac{1}{2}\). What is -3-3? What is \(\displaystyle -\frac{1}{2}-\frac{1}{2}\)? Do you see that this is just "a+ a" with \(\displaystyle a= -3\frac{1}{2}\)? Do you see that a+ a= 2a?
The third is \(\displaystyle -3\frac{1}{2}+ 3\frac{1}{2}\). Boy is that easy! What is -a+ a for any a?
The fouth is \(\displaystyle -3\frac{1}{2}+ (-5)\). Do you see that this is the same as \(\displaystyle 3\frac{1}{2}- 5\)? Do you see that -a- b= -(a+ b)? What is \(\displaystyle 3\frac{1}{2}+ 5\). Do you see that you can do this either as \(\displaystyle -\left( 3\frac{1}{2}+ 4\frac{2}{2} \right )\) or as \(\displaystyle -\left(\frac{7}{2}+ \frac{10}{2}\right)\)?
The first is \(\displaystyle -3\frac{1}{2}- (-5)\). Do you understand that -(-5)= 5? Do you see that \(\displaystyle -3\frac{1}{2}+ 5\) is the same as 5 minus \(\displaystyle 3\frac{1}{2}\)? Do you understand that \(\displaystyle 5= 4\frac{2}{2}\)? Can you do \(\displaystyle 4\frac{2}{2}- 3\frac{1}{2}\)? Or (a different way of doing the same subtraction) \(\displaystyle \frac{10}{2}- \frac{7}{2}\)? Do you see where \(\displaystyle \frac{10}{2}\) and \(\displaystyle \frac{7}{2}\) came from?
The second problem is \(\displaystyle -3\frac{1}{2}-3\frac{1}{2}\). What is -3-3? What is \(\displaystyle -\frac{1}{2}-\frac{1}{2}\)? Do you see that this is just "a+ a" with \(\displaystyle a= -3\frac{1}{2}\)? Do you see that a+ a= 2a?
The third is \(\displaystyle -3\frac{1}{2}+ 3\frac{1}{2}\). Boy is that easy! What is -a+ a for any a?
The fouth is \(\displaystyle -3\frac{1}{2}+ (-5)\). Do you see that this is the same as \(\displaystyle 3\frac{1}{2}- 5\)? Do you see that -a- b= -(a+ b)? What is \(\displaystyle 3\frac{1}{2}+ 5\). Do you see that you can do this either as \(\displaystyle -\left( 3\frac{1}{2}+ 4\frac{2}{2} \right )\) or as \(\displaystyle -\left(\frac{7}{2}+ \frac{10}{2}\right)\)?