In the proportion a/b = c/d, which expression represents the cross product?

In the proportion a/b = c/d, which expression represents the cross product?

• A. ad = bc
• B. ab = cd
• C. ac = bd
• D. bd = ac

Answer: (A)

When a/b = c/d, the two cross products — the product of the extremes and the product of the means — must be equal. Clearing denominators by multiplying both sides by bd gives ad = bc. So the relation that expresses the cross products is ad = bc. The other forms don’t pair the ends correctly: multiplying numerators and denominators together (ab = cd) isn’t what the proportion requires, and pairing a with c and b with d (ac = bd) mixes terms from the left and right sides in the wrong cross pattern. Even though bd = ac is the same as ac = bd, it still doesn’t reflect the standard cross-product pairing ad and bc.

When a/b = c/d, the two cross products — the product of the extremes and the product of the means — must be equal. Clearing denominators by multiplying both sides by bd gives ad = bc. So the relation that expresses the cross products is ad = bc.

The other forms don’t pair the ends correctly: multiplying numerators and denominators together (ab = cd) isn’t what the proportion requires, and pairing a with c and b with d (ac = bd) mixes terms from the left and right sides in the wrong cross pattern. Even though bd = ac is the same as ac = bd, it still doesn’t reflect the standard cross-product pairing ad and bc.