\(\frac{a}{b} = \frac{c}{d} ~~and~~\frac{a}{b}=\frac{a+c}{b+d} \)
How come adding the numerators of those 2 equivalent fractions always simplifies down to the same fraction?
Why does this work? It works with observation, but I'd like someone to help me make sense of this.
I did some research, and this aparently is a popular proportional manipulation. But anyways. Please explain.
+118673 That is an interesting question.
I'll take a look
\(\frac{a}{b}=\frac{ak}{bk}=\frac{c}{d}\\ so\\ \frac{a+c}{b+d}=\frac{a+ak}{b+kb}=\frac{a(1+k)}{b(1+k)}=\frac{a}{b} \)
Are you happy with that? Of course this only works if k is not equal to -1. 
+218 Ohhhh That (1+k) cancels!!
Thank you, Melody!
(Also that person was me... but I forgot I wasnt logged in)
