c-d / d-c

Question

I know the answer is -1, but what is the math that I have to show to get to that answer?

Thanks!

Answer 1

factor the top

c-d
= -1(-c+d)
= -1(d-c)

then ....
c-d / d-c
= -1(d-c)/(d-c) = -1

Answer 2

Thank you!

Answer 3

So, can I ask one more thing?
Why do you factor first?

Is it so that you have to factor to switch the order of the variables?

Why can I not just do this? (other than because I will get the wrong answer!) :)

c-d/d-c

-d+c/d-c

Is c-d not the same as -d+c?

The reason I ask is because when I fill it in with numbers, it works:

c-d; let's say this equals 4-5, which would equal -1...

Then -d+c would equal -5+4 and still equal -1....

So that's why I'm confused.

I hope that makes sense.

Thanks sgain

Answer 4

yes, c-d is the same as -d+c

but your question started with
(c-d)/(d-c)
which is
(-d + c)/(d - c)

I factored out the -1 , so my two brackets would be the same, and that you could see that I could just cancel them, leaving the -1

or you could see that in
(-d + c)/(d - c)
the numerator and denominator are opposites of each other and just like
-5 ÷ 5 = -1
27 ÷ -27 = -1
(-d + c)/(d - c) = -1

Answer 5

OK - I get it now! Thank you so much!

Answer 6

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