Comments on: When a minus times a minus equals a plus

By: Stefan Hyltoft

Stefan Hyltoft — Thu, 18 Aug 2011 17:53:18 +0000

simon lee :
i got this explanation from 6th grade textbook
2 x 3 = 4
2 x 2 = 2
2 x 1 = 0
2 x -1 = -2
2 x -2 = -4
this tells you why + x – equals to negative
in a same way
-3 x 3 = -9
-3 x 2 = -6
-3 x 1 = -3
-3 x 0 = 0
-3 x -1 = 3
-3 x -2 = 6
the pattern explains – x – equals to positive

Thank you simon I have just been looking for this kind of example, an number line example sort of. All the other examples have been confusing or not common sense to me.

By: simon lee

simon lee — Wed, 06 Apr 2011 02:04:08 +0000

i got this explanation from 6th grade textbook

2 x 3 = 4
2 x 2 = 2
2 x 1 = 0
2 x -1 = -2
2 x -2 = -4

this tells you why + x – equals to negative
in a same way

-3 x 3 = -9
-3 x 2 = -6
-3 x 1 = -3
-3 x 0 = 0
-3 x -1 = 3
-3 x -2 = 6

the pattern explains – x – equals to positive

By: Abhishek

Abhishek — Wed, 01 Dec 2010 08:01:41 +0000

I think the best answer is because ” It has been fixed to be so as a convention”. Negative numbers, like Complex numbers are after all artificial constructs used in the study of physical phenomena and maths by us, humans. Instead of looking too much to justify each and every one of our formulas and conventions, we should accept them to be so.

By: Jack

Jack — Sun, 23 May 2010 10:02:11 +0000

Another Soln

This is not a proof, however a demonstration for a curious kid why negative times negative is positive. It may be helpful to think that when dealing with the numbers ‘-’ or ‘+’ signs are identical to ‘-1 times’ or ‘+1 times’. Here is an example:

-5 = ‘-1 times’ 5

A number plus a negative number can result zero. Lets take the number ‘1’ that is ‘+1’, then take ‘-1’. It could have been any other number. The MAIN assumption is:

1 -1 = 0
Without losing the effect we can times the equation by ‘-’ or ‘-1’ then:
-1 -(-1) = 0

Since both equations are the same, that means:
-1 -(-1) = 1 -1

that means:
-(-1) = 1

it shows:

‘-’ times ‘-’ is plus
—————————————————-
This approach is also helpful to show why ‘+’ times ‘-’ is ‘-’

Let us safely assume ‘1’, which is ‘+1’, times a number results in the number, i.e. ‘1 times’ 10 is 10. Then ‘1 times’ ‘-1’ is ‘-1’ . That is:

‘+1 times’ -1 = -1

That shows: ‘-’ times ‘+’ results ‘-’
————————————————-

By: Jack

Jack — Mon, 10 May 2010 05:44:46 +0000

1 * a = a, – – ”here ‘a’ is any number”
hence, 1 * (-1) = (-1)
also -1 * a = -a, – -”here ‘a’ is any number”
hence, -1 * (-1) = – (-1)
Negative of +1 = -1
negative of (-1) = 1, because a number plus the negative of the
number adds up to zero. i.e. -1 + x = 0, that means x=1
From above, (-1) * (-1) = – (-1) = negative of (-1) = 1
That shows (minus * minus ) yields plus

By: maths 10/07/2009 | Dave

maths 10/07/2009 | Dave — Wed, 07 Oct 2009 01:20:18 +0000

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By: Dave

Dave — Tue, 06 Oct 2009 02:12:24 +0000

Nice one Denise.
Maybe in a class you could have a number of fake notes – red being a $5 iou so the value is -$5, black being $5 cash. Students can work out their value based on how many of each they have. The teacher either takes some notes or gives some notes to students (of one colour). Taking is a negative operation so taking 3 means -3 * the value of the notes. So if the notes were black the student’s value would be reduced, if the notes were red the student’s value would be increased.

I think the idea is good – probably could have explained it better.

By: Denise

Denise — Sat, 03 Oct 2009 14:38:03 +0000

The best analogy I have heard is to imagine a money box stuffed with checks (payments to you, which increase your net worth and thus are positive) and bills (payments you owe, which decrease your net worth and thus are negative. Depending on how business goes each day, you add or subtract to your total value:

Received three checks for $5 each,
+3 x +5 = +15, net increase.

Gave back (refunded or canceled) three checks for $5 each:
-3 x +5 = -15, net decrease.

Received three bills for $5 each:
+3 x -5 = -15, net decrease.

Gave back (canceled) three bills for $5 each:
-3 x -5 = +15, net increase!!

By: Gavin

Gavin — Wed, 30 Sep 2009 14:11:42 +0000

This is one of the approaches I take with my students, generally _after_ it’s been taught and I just want them to feel like it makes sense.

5 x 7 = 35

-5 x 7 must be -35
5 x -7 must be -35

The rationale: -5 x 7 can’t be the same as 5 x 7. You can’t just make one of the numbers negative and not have it affect the result.

Finally:

-5 x -7 can’t be -35 (that would be -5 x 7 or 5 x -7)
so it must be 35.

It’s kind of logical.

By: Why a negative times a negative is a positive « Hans Gilde’s weblog

Why a negative times a negative is a positive « Hans Gilde’s weblog — Wed, 30 Sep 2009 14:11:11 +0000

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