Parsing an English to Math expression question, is this ambiguous?

Solution 1:

It's definitely ambiguous, and all three readings you mentioned are possible. I would contact the vendor. But as I'm a computer scientist and native English speaker, below I've given my opinion on what the problem should have said for each equation you listed.

• "(1/5) * x", I would expect to read "The product of one-fifth and a number."
• "1/(5x)", I would expect to read exactly what the problem states, "The quotient of one and five times a number."
• "(1x)/(5x)", I would expect an even more ambiguous sentence: "The quotient of one times a number and five times a number."

Solution 2:

As alasher says, the statement as it stands is ambiguous and there are all those possible readings. Since you mentioned pauses, curiously the ambiguities can all be resolved by indicating the pause(s) with one or more commas:

1. The quotient of one, and five times a number (must mean 1/(5x))
2. The quotient of one and five, times a number (must mean 1/5 * x, or x/5)
3. The quotient of one, and five, times a number (must mean x/5x)

That said, I dislike 3 and feel it would be argued by anyone who didn't write down the right answer.