Absolute value on the top of a fraction

Question

What is the answer to a question similar to this one, where the absolute value bars are only around the numerator of the fraction?

$$\frac{|2+4(2)|}{5-10}$$

Would the fraction be equal to $\frac{10}{-5}$ and would the answer just be $-2$?

Thanks

Answer 1

Here are the possible configurations: $$\frac{|1-2|}{1-2} = \frac{|-1|}{-1}=\frac{1}{-1} = -1$$

$$\frac{|1-2|}{|1-2|} = \frac{|-1|}{|-1|}=\frac{1}{1} = 1$$

$$\frac{1-2}{|1-2|} = \frac{-1}{|-1|}=\frac{-1}{1} = -1$$

$$\frac{1-2}{1-2} = \frac{-1}{-1}=\frac{-1}{-1} = 1$$

Answer 2

You've done right! But, this is from where the concept comes from: $$| x| =\begin{cases} x & x >0 \\ 0 & x = 0 \\ -x & x < 0 \end{cases} $$

So, when you have: $|-1|$ you will simply write this as: $1$ as this obeys the third condition of the above general case. [as an example]

Once you understand this general case, it will be easy for you to move on in this topic.