Comments on: Minus or Negative?

By: Tom

Tom — Thu, 15 Oct 2020 12:30:33 +0000

Hi MathedUp.

WIth 5 x -3, if thought of as “5 lots of negative 3”, this is tangible as it is.

With -3 x 5, if thought of as “negative 3 lots of 5”, this is hard to vizualize, as in what does “negative 3 lots of” mean in concrete terms?

The only explanation I can find online that appears reasonable as a concrete model, is to treat the negative sign of the first number as subtraction, ie:

(-3) x 5 = subtract 3 lots of 5.

If there was a way to model (-3) x 5 in a concrete way, and leave the negative sign as a property of the first number, I would love to hear it. I know we can use the commutative law, and change the order of the numbers, to 5 x (-3). This is also a proper explanation, but is not a model of (-3) x 5.

Thanks

By: Mohammad

Mohammad — Sun, 28 Jan 2018 20:20:28 +0000

-3 here “-” is a unary operator whereas in 4-3, “-” is a binary operator. In the former when you say minus three you refer to the process by which negative three is obtained but when you say negative three you refer to the object itself. There is no way to denote negative three without the minus operator, either in unary or binary usage. Although one might say the unary one could be seen as zero minus three hence being a binary. Nonetheless, “-” is an operator and -3 is not a monolithic object but rather a process through which the object of negative three can be applied in arithmetic and elsewhere. Assuming what I said is true, -3 can be read minus three or negative three, like reading 2^(0.5) as square (second) root of 2 (object) or two to (the power) half (process).

I should mention that I am not a mathematician and English is not my mothe tongue. I have a degree in Physics and Two masters in Engineering. So my comment is my lay understanding of the matter and may not live up to the standard rigour of the Maths folks!

By: MathedUp

MathedUp — Tue, 09 Jan 2018 22:45:59 +0000

In reply to Tom.

Hi Tom. Thanks for commenting. I understand where you are coming from but I have a counter-argument. How about if it was “five multiplied by negative three” ie.

5 x -3

If you write that in the way you suggested, this would lead to

5 x 0 – 3

We could argue that we now need brackets around the “0 – 3” however would this lead to further confusion? Would be interested in your thoughts..

By: Tom

Tom — Fri, 05 Jan 2018 14:05:26 +0000

How about the following. Would you consider there is a mathematical difference between the following two statements?
(The x represents multiplication)

-3 x 5

And

0 – 3 x 5

The first is “negative three times five”.

The second is “zero minus three times five”.

I reckon that for all intents and purposes, both statements are the same thing, and it doesn’t matter whether the “-“ sign is read as:
(1) A property of the negative 3, or
(2) An operator on the positive 3

Happy to hear an alternate opinion, but would also like to hear whether you think that for school students of age 12 to 13 (or so), why the above would not be a reasonable explanation.

I reckon the above could help students visualize repeated subtraction, when multiplying by a negative number, as in the following.

First, Repeated Addition:
3 x 5 =
0 + 3 x 5 =
Zero PLUS 3 lots of 5 =
0 + 5 + 5 + 5 = 15.

Repeated Subtraction:
-3 x 5 =
0 – 3 x 5 =
0 MINUS 3 lots of 5 =
0 – 5 – 5 – 5 = -15

By: MathedUp

MathedUp — Mon, 15 May 2017 16:29:02 +0000

In reply to Oliver Gray. Agree!

By: Oliver Gray

Oliver Gray — Mon, 15 May 2017 14:08:15 +0000

I think it’s a really important distinction to make, and try to emphasise it by writing the negative sign as a superscript proceding the digit, wheras I write the minus sign in the usual place. I think we as mathematicians ought to separate our objects from our processes, our nouns from our verbs.

By: arkalot

arkalot — Thu, 27 Apr 2017 10:47:18 +0000

In reply to MathedUp.

Maybe – but still may arise as part of a BIDMAS question 🙂

2 x 5 – 20/2 + 2 x 2

By: MathedUp

MathedUp — Mon, 10 Apr 2017 19:06:05 +0000

In reply to arkalot. A better solution would be to not use BIDMAS :)

By: arkalot

arkalot — Sun, 02 Apr 2017 13:10:14 +0000

This is all fine but there is a problem, which is why I interchange minus/negative all over the place

Consider: 20 – 10 + 4

So you say: twenty minus ten plus four

no problem you think

now use BIDMAS/BODMAS

the tendency is to do 10 + 4 = 14 then 20 – 14 = 6 but this is not the correct answer!

You need to do -10 + 4

So is it negative 10 or minus 10? (thats why I tell kids to work L – R for +/- only questions)

By: Matt Rosenberg

Matt Rosenberg — Mon, 20 Mar 2017 11:52:25 +0000

I find it’s best to mix them up, not only for real life resilience but also because they are essentially the same thing. 3x*-2 = -6x “Three x multiplied by negative two equals negative 6x” but 3x(y – 2) = 3xy – 6x, here you need to do the same calculation when you expand the bracket but you are much more likely to read the second term as “minus six x” or “subtract six x” because of the first term.