If a,b,c, and f are four nonzero numbers, then all of the following proportions are equivalent EXCEPT a/f=b/c, f/c=b/a, c/a=f/b, a/c =b/f, and af/bc=1/1

Question

anonymous · Answer

so first we start with the information that we can use:

since we know that: 

$$af/bc = 1/1$$

then:

$$af= bc$$

now from the above statement we can make the following expressions:

first, if we divide both sides by c and both sides again by f, we get:

$$a/c= b/f$$

Second,  if we divide both sides by a and both sides again by b, we get:

$$f/b= c/a$$

Third,  if we divide both sides by a and both sides again by c, we get:

$$f/c= b/a$$

Now, the only form we will not be able to get is:

$$a/f= b/c$$

just because if we cross multiply, we will get:

$$ac=fb$$

which does not agree with the first statement we made at the beginning, that is:

IF:

$$af/bc = 1/1$$

then:

$$af= bc$$

Do you get it?

anonymous · Answer

yeah, i get it. thanks :D