Math debate

[LinRTX]

What is the difference in the phrase "multiply by a factor of 1.75" and "increase by a factor of 1.75"? Are they the same? Please explain your answers. We are having an interesting discussion at our house.

[chiguirre]

I think that multiply is (x * 1.75) and increase is (x + 1.75x) but that's just me.

[Paige]

43 minutes ago, chiguirre said:

I think that multiply is (x * 1.75) and increase is (x + 1.75x) but that's just me.

I agree about the term increase usually being for addition, but it's confusing because factor is a multiplication term. I'd probably multiply for both.

[Farrar]

My impulse would be to multiply both... but I'm swayed by Chiguirre's definition. But it wouldn't have immediately occurred to me. I would have just been confused by the wording then eventually decided to multiply it.

[RootAnn]

I would say that as long as you are not dealing with percentages, they are considered to mean the same thing.

https://www.beatthegmat.com/word-translation-when-x-increases-by-a-factor-of-4-t112477.html

If you were dealing with percentages, I would go with chiguirre's definition.

[ieta_cassiopeia]

My understanding is that "factor" is a scalar operation. Its purpose in the sentence is to tell you the number needs to go up/down by a proportion of itself,. rather than an absolute amount. Its presence in the sentence tells us that it is not an addition or a subtraction.

It does not by itself identify with direction to take the number. So if you hypothetically got a question that said, "Change 28 by a factor of 1.75", you can answer thus:

"It's either 49 (if multiplied) or 16 (if divided), and by the way please tell the author to come up with more sensible problems".

The "increase" is the part that forces this to be a multiplication rather than a division, so "Increase 28 by a factor of 1.75" will be 49. It's also a sentence structure that has been criticised for unclear/inefficient by people who know a lot more about maths than me. So feel free to use this as a teachable moment for why it is important that maths be presented clearly, as well as logically. In most contexts, it's not enough for numbers and working to be unambiguous - they should also look unambiguous, so that everyone involved can be on the same wavelength and comment with understanding.

[letsplaymath]

Language is inherently vague, at least as compared to math. This discussion shows that the same words can mean quite different things to different people.

My vote for the meaning of "increase by a factor of 1.75" would go with the addition crowd, because this reminds me of computing interest. Your principal increases by a factor we call the interest rate, and the equation looks like:

• New amount = Principal x (1 + rate)

But of course, whoever originally made the statement may mean 1.75 to be the "1 + rate" in that equation, which would put him in the multiplication camp.

If you're dealing with a textbook question, answer according to how the author is interpreting the words, if you can figure that out from context.

Edited February 1, 2020 by letsplaymath