Adding a fraction to a whole number in an algebraic equation

Feb 2018
4
0
Haiproso
Hello! :)

I am going over another answer for a question on an online test:
algebra.PNG
The only question I have is, how did they get 9/2? The way I'd go about solving this is making the -4 a -4/1, and then adding -1/2 to get 4/2. Where am I going wrong?

Thanks in advanced! :)
-Neo
 

Prove It

MHF Helper
Aug 2008
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4,999
$\displaystyle \begin{align*} -\frac{1}{2} - 4 &= - \left( \frac{1}{2} + 4 \right) \\ &= - \left( \frac{1}{2} + \frac{8}{2} \right) \\ &= -\frac{9}{2} \end{align*}$
 
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Feb 2018
4
0
Haiproso
I'm sorry, I still don't get it... I know that -1/2 + 4 = -(1/2 + 4), but to get 8/2, did you multiply 4/1 by 2? And if so, why? Is it because 2 is the denominator?

Thank you for your efforts! ^^
-Neo
 

Plato

MHF Helper
Aug 2006
22,470
8,640
I'm sorry, I still don't get it... I know that -1/2 + 4 = -(1/2 + 4), but to get 8/2, did you multiply 4/1 by 2? And if so, why? Is it because 2 is the denominator?
First: $\large{ - \frac{1}{2} + 4 \ne - \left( {\frac{1}{2} + 4} \right)}$

Can you do this $\dfrac{8}{2} - \dfrac{1}{2}~?$