Math

[BabaT]

Please kindly help me out with this question. Thanks.

 

[Dr.Peterson]

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?

 

[BabaT]

ok i did not know

 

[HallsofIvy]

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 $\displaystyle -\left(\frac{7}{2}+ \frac{10}{2}\right)$?