# Negative numbers: “minus” or “negative”?

I noticed that when negative number are used in speech, there are two dominant patterns. Taking "-10" as an example, in some cases it is pronounced "negative ten", while in others it is "minus ten".

I could not find any rules for this. A discussion in MathOverflow (which was closed) suggested that using negative was introduced in the US by "New Math" since the 1960's. If this is true, I would expect non-American speakers to mainly use minus (which I think is similar to the usage in most foreign languages), and perhaps senior Americans as well.

I'm not asking for opinions about this argument here. I'm also not looking for explanations or reasons for preference of one or another or the like.

I am looking for

1. References for authoritative text if there is any

2. Evidence of usage: I'd like to know how different dialects call negative numbers, and if there are rules or conventions for using e.g. "minus 40" or "negative 40" in different contexts in the same dialect.

• I think you'll find your answer is that both are used, and if there are conventions, they are unique to each classroom, not to the subject as a whole. In all my years of math instruction, saying "minus 10" was perfectly acceptable for "negative 10". – Andrew Jan 10 '18 at 22:34
• **groan** I'm really not sure what some of those Math Overflow answers are talking about. How can anyone blame New Math when this sense of "negative" was around 300 years prior, in the 1660s? – Laurel Jan 10 '18 at 23:58

Probably this extract from Merriam-Webster's Guide to Everyday Math may help:

Among the more commonly confused mathematical terms, minus and negative have the dubious honor of confounding teachers as well as students. The word minus refers to the operation of subtraction, not to negative numbers.

• This seems to be US usage. In UK we never say "negative 10". It means "there is nothing here with 10" or similar. The number `-10` is said as minus 10. – Weather Vane Jan 10 '18 at 22:02
• @WeatherVane it's the same in the US. "Minus 10" is common. Most students can tell from context whether the speaker is referring to subtraction or a negative number. I think this M-W guide is optimistic, not realistic. – Andrew Jan 10 '18 at 22:30
• Thanks for the reference @user159691, this is (sorry of) the kind of authoritative text I was looking for. Still looking for more. – laugh Jan 11 '18 at 7:38

There is a difference here between common practice and good practice.

It is good mathematical practice to distinguish between positive and negative numbers, which entails that you should say "negative ten" for the number that is ten less than zero. It is also good mathematical practice to say "minus ten" if you mean to subtract positive ten from something.

Because, however, the minus sign is used in mathematics to designate (1) negative numbers, (2) the operation of subtraction, and (3) additive inverses, it is very common for people, even mathematicians, to use "minus" in speech indiscriminately for all three.