You just do the division of absolute values (remove the negative sign) and then add the negative sign to the result. That's HOW. I suspect you really mean "how is it possible that a positive number could be divided by a negative number?", which is more subtle: it's an abstract operation, as are most mathematical operations. When we teach division to children, we take (for example) 10 teddy bears and separate them into two groups, and show the child that there are 5 bears in each group. That's "division by 2", the child is told. But that's only a very special kind of division which involves no fractions, no negative numbers, and no non-real numbers. It's a mistake to think you can do that with "negative teddy bears" or something. The operation is abstract, and can't be mapped to something as physically concrete as separating bears into groups.

Thanks, you are right I was trying to think of a phisical situation where this might be possible and getting very confused - all because my 11 year old had a question about it in maths!

In 50 to 50 partnership of 2 partners, 2 partners are liable for it, it is divided by 2 partners It is 4 cases of Increase of Positive(Credit, Fortune) Decrease of Negative(Debt, Bill) Decrease of Positive(Credit, Fortune) -> [ (+N) / (-N) ] Increase of Negative(Debt, Bill) { 4 Basic Arithmetic Operations } Coupdetat.net (2009.03.10) 0. [ Zero ( 0 ) ] = [ We have no (Partial Fortune and Debt) ], [ Zero ( 0 ) is not (dead one) but (living one). ] 1. Increase of Positive(Credit, Fortune) [ + (+2) + (+2) + (+2) ] = [ + { (+2) + (+2) + (+2) } ] = [ + (+6) ] = [ (+6) ]-> (Self-employed) [ (+2) X (+3) ] = [ + { (+2) X (3) } ] = [ + (+6) ] = [ (+6) ]-> (Self-employed) [ (+12) ÷ (+2) ] = [ + { (+12) ÷ (2) } ] = [ + (+6) ] = [ (+6) ]-> (2 Partnership) 2. Decrease of Negative(Debt, Bill) -> (Offset) * [ (-6) - (-6) = ( 0 ) ] [ - (-2) - (-2) - (-2) ] = [ - { (-2) + (-2) + (-2) } ] = [ - (-6) ] = [ (+6) ]-> (Self-employed) [ (-2) X (-3) ] = [ - { (-2) X (3) } ] = [ - (-6) ] = [ (+6) ]-> (Self-employed) [ (-12) ÷ (-2) ] = [ - { (-12) ÷ (2) } ] = [ - (-6) ] = [ (+6) ]-> (2 Partnership) 3. Decrease of Positive(Credit, Fortune) [ - (+2) - (+2) - (+2) ] = [ - { (+2) + (+2) + (+2) } ] = [ - (+6) ] = [ (-6) ]-> (Self-employed) [ (+2) X (-3) ] = [ - { (+2) X (3) } ] = [ - (+6) ] = [ (-6) ]-> (Self-employed) [ (+12) ÷ (-2) ] = [ - { (+12) ÷ (2) } ] = [ - (+6) ] = [ (-6) ]-> (2 Partnership) 4. Increase of Negative(Debt, Bill) [ + (-2) + (-2) + (-2) ] = [ + { (-2) + (-2) + (-2) } ] = [ + (-6) ] = [ (-6) ]-> (Self-employed) [ (-2) X (+3) ] = [ + { (-2) X (3) } ] = [ + (-6) ] = [ (-6) ]-> (Self-employed) [ (-12) ÷ (+2) ] = [ + { (-12) ÷ (2) } ] = [ + (-6) ] = [ (-6) ]-> (2 Partnership) 5.Times , [ Number = N ], [ (-N) = Negative number ], [ (+N) = Positive number ] [ X (-N) ] = [ Subtract a thing added to N times. ] -> The meaning of (-N) is not debt but times. [ X (+N) ] = [ Add a thing multiplied by N. ] -> The meaning of (-N) is not fortune but times. [ ÷ (-N) ] = [ Subtract a thing divided by N. ] -> The meaning of (-N) is not debt but times. [ ÷ (+N) ] = [ Add a thing divided by N. ] -> The meaning of (-N) is not fortune but times. 6. Law of Liuhui Brahmagupta [ N X (+N) ] = [ + ( N X N ) ], [ N X (-N) ] = [ - ( N X N ) ] [ N ÷ (+N) ] = [ + ( N ÷ N ) ], [ N ÷ (-N) ] = [ - ( N ÷ N ) ] [ (+N) ] = [ + (+N) ] = [ - (-N) ] = [ (N) ], [ (-N) ] = [ - (+N) ] = [ + (-N) ] [ - ( 0 ) ] = [ + ( 0 ) ] = [ ( 0 ) ], [ + N - N ] = [ + ( N - N ) ] = [ ( N - N ) ] [ - N - N ] = [ - ( N + N ) ], [ - N + N ] = [ - ( N - N ) ] Commutative law of < - N > and < + N > is (Natural). http://www.youtube.com/user/trapassing http://www.flickr.com/photos/trapassing I cannot english. 1/5. [ Copyright of Image and Sentence ] 2/5. Copyright Notice : Copyright © (Coupdetat.net) 3/5. Do not Editing 4/5. Free Copyright (Use Only) : Personal Homepage and Blog 5/5. Copyright (No Use) : Profit-Making, Enterprise, Government

(revision) -------------------------------------------------------- How can a positive number be divided by a negative number? [ (Positive) ÷ (Negative) ], Example ---------------------------------------------------- (Conclusion) 5-3. Decrease of Fortune ( Positive, Credit ) [^^^] = [ (+12) ÷ (-2) = (-6) = { - (+6) } ] = [ (+12) / (-2) = (-6) ] = [ { (+12) / (+1) } X { (+1) / (-2) } = (-6) ] = [ { (+12) } X { (-0.5) } = (-6) ] = [ (+12) X (-0.5) = (-6) ] = [ - { (+12) X (0.5) } = (-6) ] * [ N X (-N) ] = [ - ( N X N ) ] = [ - { (+6) } = (-6) ] = [ - (+6) = (-6) ] * [ - (+N) ] = [ + (-N) ] = [ (-N) ] = [ + (-6) = (-6) ] * (Addition sign) = (Adding up) = [ (-6) = (-6) ] (1) [ (+12) ÷ (-2) = (-6) = { - (+6) } ] In 50 to 50 partnership of 2 partners, they buy goods in fortune($12) for cash and have Decrease of Fortune($12), divide it into two equal parts and subtract it. (2) [ (+12) X (-0.5) = (-6) = { - (+6) } ] In 50 to 50 partnership of 2 partners, they buy goods in fortune($12) for cash and have Decrease of Fortune($12), Because share of 1 person (One side) is half(0.5), one side multiplies fortune($12) by (0.5) and subtracts it. ----------------------------------------------------- In 50 to 50 partnership of 2 partners, 2 partners are liable for it, it is divided by 2 partners It is 4 cases of Increase of Positive(Credit, Fortune) Decrease of Negative(Debt, Bill) Decrease of Positive(Credit, Fortune) -> [ (+N) / (-N) ] Increase of Negative(Debt, Bill) ----------------------------------------------------- * (-N) = Negative number, (+N) = Positive number * Division = (÷) = (/) -------------------------------------------------- 1. [ Negative X Negative = Positive ], Proof [^^^] = [ Negative numer X Negative number = Positive number ] = [ Negative X Negative = Positive ] = [ (Negative) X (Negative) = (Positive) ] = [ (-N) X (-N) = (+N) ] = [ { (-N) } X { (-N) } = (+N) ] = [ { (+N) + (-2N) } X { (+N) + (-2N) } = (+N) ] = [ { (+N) - (+2N) } X { (+N) - (+2N) } = (+N) ] = [ { (+N) - (+2N) } X (+N) - { (+N) - (+2N) } X (+2N) = (+N) ] = [ { (+N^2) - (+2N^2) } - { (+2N^2) - (+4N^2) } = (+N) ] = [ { (+N^2) - (+2N^2) } - { (+2N^2) + (-4N^2) } = (+N) ] = [ (+N^2) - (+2N^2) - (+2N^2) - (-4N^2) = (+N) ] = [ (+N^2) - (+2N^2) - (+2N^2) + (+4N^2) = (+N) ] = [ (+N^2) + (+4N^2) - (+2N^2) - (+2N^2) = (+N) ] = [ { (+N^2) + (+4N^2) } - { (+2N^2) + (+2N^2) } = (+N) ] = [ { (+5N^2) } - { (+4N^2) } = (+N) ] = [ (+5N^2) - (+4N^2) = (+N) ] = [ (+N^2) = (+N) ] = [ (+N) = (+N) ] = [ (N) = (N) ] = [ N = N ] 2. [ (+N) ÷ (-N) = (-N) ], Proof [^^^] = [ (-N) X (-N) = (+N) ] = [ { (-N) } X (-N) = (+N) ] = [ { (-N) } = (+N) ÷ (-N) ] = [ (-N) = (+N) ÷ (-N) ] = [ (+N) ÷ (-N) = (-N) ] 3. [ (-N) X (-N) = { - (-N) } = (+N) ] -> Extinguishment of obligation (Offset) 4. Example of division 4-1. [ (+N) ÷ (+N) = (+N) ], Example [^^^] = [ (+N) ÷ (+N) = (+N) ] = [ (+12) ÷ (+2) = (+6) ] = [ (Money $12) ÷ (2 Persons) = (Money $6) ] 4-2. [ (-N) ÷ (+N) = (-N) ], Example [^^^] = [ (-N) ÷ (+N) = (-N) ] = [ (-12) ÷ (+2) = (-6) ] = [ (Debt $12) ÷ (2 Persons) = (Debt $6) ] 4-3. [ (-N) ÷ (-N) = (+N) ], Example [^^^] = [ (-N) ÷ (-N) = (+N) ] = [ (-12) ÷ (-2) = (+6) ] = [ (Debt $12) ÷ (Debt $2) = (6 bundles ] 4-4. [ (+N) ÷ (-N) = (-N) ], Example -> Sophistry [^^^] = [ (+N) ÷ (-N) = (-N) ] = [ (+12) ÷ (-2) = (-6) ] = [ (Money $12) ÷ (Debt $2) = (Debt $6) ] ---> ????????? ------------------------------------------------------------- 5. Change (Fraction) for (Frime number). 5-1. Increase of Fortune ( Positive, Credit ) [^^^] = [ (+12) ÷ (+2) = (+6) = { + (+6) } ] = [ (+12) / (+2) = (+6) ] = [ { (+12) / (+1) } X { (+1) / (+2) } = (+6) ] = [ { (+12) } X { (+0.5) } = (+6) ] = [ (+12) X (+0.5) = (+6) ] = [ + { (+12) X (0.5) } = (+6) ] * [ N X (+N) ] = [ + ( N X N ) ] = [ + { (+6) } = (+6) ] = [ + (+6) = (+6) ] * (Addition sign) = (Adding up) = [ (+6) = (+6) ] = [ (6) = (6) ] = [ 6 = 6 ] (1) [ (+12) ÷ (+2) = (+6) = { + (+6) } ] In 50 to 50 partnership of 2 partners, they sell goods in $12 for cash and have Increase of Fortune($12), divide it into two equal parts and add it. (2) [ (+12) X (+0.5) = (+6) = { + (+6) } ] In 50 to 50 partnership of 2 partners, they sell goods in fortune($12) for cash and have Increase of Fortune($12), Because share of 1 person (One side) is half(0.5), one side multiplies fortune($12) by (0.5) and adds it. 5-2. Decrease of Debt ( Negative, Bill ) [^^^] = [ (-12) ÷ (-2) = (+6) = { - (-6) } ] = [ (-12) / (-2) = (+6) ] = [ { (-12) / (+1) } X { (+1) / (-2) } = (+6) ] = [ { (-12) } X { (-0.5) } = (+6) ] = [ (-12) X (-0.5) = (+6) ] = [ - { (-12) X (0.5) } = (+6) ] * [ N X (-N) ] = [ - ( N X N ) ] = [ - { (-6) } = (+6) ] = [ - (-6) = (+6) ] * [ - (-N) ] = [ + (+N) ] = [ (+N) ] = [ + (+6) = (+6) ] * (Addition sign) = (Adding up) = [ (+6) = (+6) ] = [ (6) = (6) ] = [ 6 = 6 ] (1) [ (-12) ÷ (-2) = (+6) = { - (-6) } ] In 50 to 50 partnership of 2 partners, they owe debt ($12) in customer of offset, divide it into two equal parts and subtract it. (Offset) (2) [ (-12) X (-0.5) = (+6) = { - (-6) } ] In 50 to 50 partnership of 2 partners, they owe debt ($12) in customer of offset, Because share of 1 person (One side) is half(0.5), one side multiplies debt($12) by (0.5) and subtracts it. (Offset) 5-3. Decrease of Fortune ( Positive, Credit ) [^^^] = [ (+12) ÷ (-2) = (-6) = { - (+6) } ] = [ (+12) / (-2) = (-6) ] = [ { (+12) / (+1) } X { (+1) / (-2) } = (-6) ] = [ { (+12) } X { (-0.5) } = (-6) ] = [ (+12) X (-0.5) = (-6) ] = [ - { (+12) X (0.5) } = (-6) ] * [ N X (-N) ] = [ - ( N X N ) ] = [ - { (+6) } = (-6) ] = [ - (+6) = (-6) ] * [ - (+N) ] = [ + (-N) ] = [ (-N) ] = [ + (-6) = (-6) ] * (Addition sign) = (Adding up) = [ (-6) = (-6) ] (ê°€) [ (+12) ÷ (-2) = (-6) = { - (+6) } ] In 50 to 50 partnership of 2 partners, they buy goods in fortune($12) for cash and have Decrease of Fortune($12), divide it into two equal parts and subtract it. (나) [ (+12) X (-0.5) = (-6) = { - (+6) } ] In 50 to 50 partnership of 2 partners, they buy goods in fortune($12) for cash and have Decrease of Fortune($12), Because share of 1 person (One side) is half(0.5), one side multiplies fortune($12) by (0.5) and subtracts it. 5-4. Increase of Debt ( Negative, Bill ) [^^^] = [ (-12) ÷ (+2) = (-6) = { + (-6) } ] = [ (-12) / (+2) = (-6) ] = [ { (-12) / (+1) } X { (+1) / (+2) } = (-6) ] = [ { (-12) } X { (+0.5) } = (-6) ] = [ (-12) X (+0.5) = (-6) ] = [ + { (-12) X (0.5) } = (-6) ] * [ N X (+N) ] = [ + ( N X N ) ] = [ + { (-6) } = (-6) ] = [ + (-6) = (-6) ] * (Addition sign) = (Adding up) = [ (-6) = (-6) ] (1) [ (-12) ÷ (+2) = (-6) = { + (-6) } ] In 50 to 50 partnership of 2 partners, they owe debt ($12) in customer of offset, divide it into two equal parts and add it. (2) [ (-12) X (+0.5) = (-6) = { + (-6) } ] In 50 to 50 partnership of 2 partners, they owe debt ($12) in customer of offset, Because share of 1 person (One side) is half(0.5), one side multiplies debt($12) by (0.5) and adds it. http://www.youtube.com/user/trapassing http://www.flickr.com/photos/trapassing I cannot english. 1/5. [ Copyright of Image and Sentence ] 2/5. Copyright Notice : Copyright © (Coupdetat.net) 3/5. Do not Editing 4/5. Free Copyright (Use Only) : Personal Homepage and Blog 5/5. Copyright (No Use) : Profit-Making, Enterprise, Government