migongoniwt

2022-06-27

If $\frac{a}{b}=\frac{c+d}{e+f}$ so $a$ is equal to $c+d$?
I have these question, a is always c+d and b is e+f ?.
Thanks.

Ryan Newman

Expert

NO.
Here is an counterexample.
$\frac{1}{2}=\frac{1+2}{3+3}$
Obviously $1\ne 1+2=3$, $2\ne 3+3=6$

veirarer

Expert

There are plenty of easy counterexamples, of course. $\frac{1}{1}=\frac{2+3}{2+3}$, but $2+3\ne 1$. But what you suggest is true if both fractions are in reduced form - that is, if $a$ and $b$ are relatively prime and $c+d$ and $e+f$ are relatively prime.