# 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.

• – user29952
Jan 10, 2018 at 21:49
• **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, 2018 at 23:58

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.

• It doesn't make sense to claim that '-' designates negative numbers: for x=-6, both `-x` and `-(-8)` are positive numbers. Reading them as 'minus x' and 'minus minus 8' is not being indiscriminate, but actually absolutely correct. On a related note, '-' should not be understood as the adjective 'negative' either, because of course `-8` does not mean that `8` is negative. I wrote more here. Oct 1, 2023 at 11:42

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. Jan 10, 2018 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. Jan 10, 2018 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. Jan 11, 2018 at 7:38
• Also, a late thank you @WeatherVane for providing the evidence of usage that I was looking for. I indeed suspected that "negative ten" is not used by British speakers. Jan 15, 2021 at 11:59
• @WeatherVane To be clear: this Answer is not claiming that `-10` is read as 'negative 10'; when we (correctly) read this as 'minus 10', the word 'minus' is not functioning as an adjective (after all, `10` is not negative) but simply indicating that `10`'s position relative to `0` is being flipped. In reading `-x` as 'minus x', there is no assumption that \$x\$ is negative (or that it is positive). Please refer to my comment under Jeff's Answer Oct 1, 2023 at 11:55

'−' is an operator, and it is pronounced 'minus'.

'Positive' and 'negative' are properties of numbers, as are 'even' and 'odd'.

−7 has the property of being an odd number, and the property of being a negative number, and has many other properties besides.

−x may or may not be an odd number or a negative number. It would therefore be completely wrong to say '−x' as 'negative odd x'. (I am listing two obvious properties to highlight the absurdity of so doing).

To say 'minus x', but 'negative seven' is confusing (as can be seen by the question posed in this thread), and absurd because it is not the properties that we list when we are saying the number, but its value.

The value of '−7' is 'minus seven', and its properties are 'negative', 'odd', ...

• Did you read the question in its entirety? Apr 24, 2022 at 17:28
• Yes. As a theoretical Physicist and Computational Chemist (now semi retired) I bow to no authority except logic. By providing an argument based on logic I was providing an as authoritative reply as possible. In my career, with many publications in such journals as Nature, and attending conferences around the world, I have never encountered "negative seven" rather than "minus seven", but there seems to be a trend on YouTube, of mainly American mathematicians, to adopt this usage. Apr 25, 2022 at 18:43
• As much as I like the distinction between properties of numbers and number name I am skeptical about the conclusion this answers draws: '-7' has indeed the property 'negative', but this doesn't mean it cannot have the name 'negative seven'. I even think, because 'negative' is a property of '-7' it makes sense to use the name of the property in the multi-word name of the number: 'negative seven'. Nov 30, 2023 at 2:48