If $\frac{a}{b}=\frac{c+d}{e+f}$ so $a$ is equal to $c+d$?

Question

I have these question, a is always c+d and b is e+f ?.

Thanks.

Answer 1

NO.

Here is an counterexample.

$$\frac{1}{2} = \frac{1+2}{3+3}$$

Obviously $1 \not = 1+2 = 3$, $2 \not = 3+3 =6$

Answer 2

There are plenty of easy counterexamples, of course. $\frac{1}{1} = \frac{2 + 3}{2 + 3}$, but $2 + 3 \neq 1$. 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.