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

Question

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

Answer 1

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

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

START WITH ANSWER E because it's equal to 1/1

& CROSS-MULTIPLY (upper-left x lower-right = upper-right x lower left)

answer (E)

af / bc = 1 / 1

1 af = 1 bc

af = bc

THEN CROSS-MULTIPLY ALL THE OTHER ANSWERS TO MATCH THAT RESULT.

answer (A)

a./ f = b / c

ac = bf WRONG

IN THIS CASE, YOU DON'T HAVE TO CROSS-MULTIPLY THE OTHER ANSWERS BECAUSE YOU FOUND THE WRONG ANSWER ON THE FIRST TRY, BUT YOU CAN CALCULATE THE REST OF THE ANSWERS FOR PRACTICE, AS FOLLOWS:

answer (B)

f / c = b / a

af = bc CORRECT

answer (C)

c / a = f / b

af = bc CORRECT

answer (D)

a / c = b / f

af = bc CORRECT

Answer 2

These are proportions. One ratio equal to another ratio.

You can flip both fractions without altering the proportion.

You can cross multiply.

You can switch one set of variables cross-wise or both sets.

 

If you write all the options and perform all the permutations, you will see that   a/f = b/c is not equivalent to the other four proportions