Sandra M.

asked • 08/23/12

How can one division expression have more than one answer?

My 5th grader is in Ag Math and they are to answer questions regarding math in their journal daily. Today's question is "Explain how one division expression can have many different answers and give an example to support your answer". We are truly stumped, we maybe overthinking the question. My daughter thinks that it could have different answers if the expression ask for an estimate or exact number. Please help!!

John H.

Questions like these, while well intentioned, cause so much confusion and misteaching. The entire purpose behind having *The Order of Operations* (which will likely be introduced in a year or two) is to make sure that when two people anywhere on the earth evaluate an expression, *they will get the same result!* The idea of having a division expression that could result in two different answers works directly against this important principle. The reason you were stumped is you intuitively were trying to honor The Order of Operations. I'm seeing answers below that suggest writing different problems with the same solution or treating a different rounding as a different answer, but that's a different matter entirely, e.g., 6 / 3 = 2 and 10 / 5 = 2. That's not what the question asked... what the question asked was how could 9 / 3 have more asnswers than 2... it can't... 9 / 3 = 3 (and only 3). If it didn't, math as we know would fall apart.


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John H.

I respectfully disagree here... a given square root has *only one* value, not two. SqRt(4) = 2, and only two. When I work with my students who think that a root can have two values, I make a bet with them... I promise to pay them $5 if they can find a calculator that will say SqRt(4) = anything besides 2. I've never lost that bet and never will because all roots *by definition* are non-zero (i.e., either zero or a positive number.) So, SqRt(4) / 2 = (+2) / 2 = +1, period. I'm not going to downvote this answer because that feels disrespectful, but the answer as written is not correct and will mislead students


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