# Adding a fraction to a whole number in an algebraic equation

#### SpaghettNeo

Hello!

I am going over another answer for a question on an online test:

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?

-Neo

#### Prove It

MHF Helper
\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*}

1 person

#### SpaghettNeo

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

#### DenisB

I know that -1/2 + 4 = -(1/2 + 4)....
No. -1/2 + 4 = -(1/2 - 4)
That's really -1(1/2 - 4)
So: -1*(1/2) = -1/2, -1*(-4) = +4

#### Plato

MHF Helper
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 $\dfrac{8}{2} - \dfrac{1}{2}~?$