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

By: maths 10/07/2009 | Dave

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

[...] crossedstreams.com » When a minus times a minus equals a plus [...]

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

[...] At Crossed Streams [...]

By: Negative times negative « The Number Warrior

Negative times negative « The Number Warrior — Tue, 29 Sep 2009 21:57:58 +0000

[...] Streams: When a minus times a minus equals a plus Walking Randomly: Why is a ‘minus times a minus equal to a plus’? Math Less Traveled: Minus [...]

By: Paul Brabban

Paul Brabban — Tue, 29 Sep 2009 20:45:14 +0000

Hey @Joe, @Ludwig, thanks for taking the time! Nice alternate views.

By: Ludwig

Ludwig — Tue, 29 Sep 2009 17:17:10 +0000

I’ve heard one which is sort of intuitive that might be interesting, perhaps you have too.

Suppose you have a transparent tank of water with an outlet with a tap at the bottom. You turn on the tap and the water begins to drain out of the tank.

Now you set up a video camera and film the tank draining out.

Take the tape and play it _backwards_.

Sort of like saying _backwards_ * _draining_ = filling where “backwards” and “draining” are “negatives” and “filling” is a “positive”.

By: Minus times minus is plus « The Math Less Traveled

Minus times minus is plus « The Math Less Traveled — Tue, 29 Sep 2009 11:56:40 +0000

[...] at crossedstreams.com gives an explanation involving two quantities with real-world interpretations associated with negative values: net worth [...]

By: Walking Randomly » Why is a ‘minus times a minus equal to a plus’?

Mon, 28 Sep 2009 01:46:33 +0000

[...] completely intuitive and so far the best I have come across is the explanation from my friend Paul over at Crossed Streams who’s fiancee asked us this very question while we were all on a night out. Other good [...]