Which Proportion is Not Equivalent in This SAT Math Problem?

[Elbobo]

Homework Statement

If a, b, c, and f are four nonzero numbers, then all of the following proportions are equivalent EXCEPT

(A) (a / f) = (b / c)
(B) (f / c) = (b / a)
(C) (c / a) = (f / b)
(D) (a / c) = (b / f)
(E) (af / bc) = (1 / 1)

Homework Equations

None

The Attempt at a Solution

The answer is A, but I have absolutely no clue why. This question doesn't even make sense. And no, there's no diagram or any other info, which makes me think that this question was an error...

 

[HallsofIvy]

Homework Statement

If a, b, c, and f are four nonzero numbers, then all of the following proportions are equivalent EXCEPT

(A) (a / f) = (b / c)
(B) (f / c) = (b / a)
(C) (c / a) = (f / b)
(D) (a / c) = (b / f)
(E) (af / bc) = (1 / 1)

Homework Equations

None

The Attempt at a Solution

The answer is A, but I have absolutely no clue why. This question doesn't even make sense. And no, there's no diagram or any other info, which makes me think that this question was an error...

Perhaps it would make more sense if you wrote it in terms of products, by multiplying on both sides by the denominators, rather than fractions.

(A) is equivalent to ac= bf.
(B) is equivalent to af= bc.
(C) is equivalent to bc= af (which, of course, is the same as af= bc).
(D) is equivalent to af= bc.
(E) is equivalent to af= bc.

Now do you see why all except (A) are equivalent?

 

[Dick]

(B)-(F) are all equivalent to af=bc. (A) is equivalent to fb=ac.