Because a minus times a minus equals a plus! It's the law! 2 x -1 would be -2 Therefore -2 x -1 could not also equal -2 The 2 minus signs cancel each other out.
Mmmmm not quite what I was after. I know the maths rules - I was just wondering how they had arrived at it - logically like, with real stuff.
this explains it clearly enough <font size="+3">Question Corner and Discussion Area </font></p><hr /><h1>Why is the Product of Negative Numbers Positive?</h1>Asked by an anonymous poster on March 18, 1997: <blockquote>I'm helping a 7th grader with things like: a plus times a plus equals a plus, a minus times a plus equals a minus, and a plus times a minus equals a minus. All OK. But when I tell him a minus times a minus equals a plus he says WHY? (sorry about yelling). I won't feel bad if you don't answer this. No textbook and nobody has the faintest idea. But just in case you do answer, please remember it's a 7th grader who wants to understand, not to mention yours truly. </p></blockquote>The answer has to do with the fundamental properties of operations on numbers (the notions of "addition", "subtraction", "multiplication", and "division". Your 7th grader's question is an important and fundamental one (which I am both surprised and sorry that he has not been able to find an answer for yet). Each number has an "additive inverse" associated to it (a sort of "opposite" number), which when added to the original number gives zero. This is in fact the reason why the negative numbers were introduced: so that each positive number would have an additive inverse. </p> For example, the inverse of 3 is -3, and the inverse of -3 is 3. </p> Note that when you take the inverse of an inverse you get the same number back again: "-(-3)" means "the inverse of -3", which is 3 (because 3 is the number which, when added to -3, gives zero). To put it another way, if you change sign twice, you get back to the original sign. </p> Now, any time you change the sign of one of the factors in a product, you change the sign of the product: </p> (-something) × (something else) is the inverse of (something) × (something else), because when you add them (and use the fact that multiplication needs to distribute over addition), you get zero. </p> For example, is the inverse of , because when you add them and use the distributive law, you get . </p> So is the inverse of , which is itself (by similar reasoning) the inverse of . </p> Therefore, is the inverse of the inverse of 12; in other words, the inverse of ; in other words, 12. </p>
Just be careful with scratch cards! http://www.manchestereveningnews.co.uk/news/s/1022757_cool_cash_card_confusion
