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- abstract algebra - Why is negative times negative = positive . . .
First, to establish that a positive times a negative is negative: $3 \times 2 = 6, 3 \times 1 = 3, 3 \times 0 = 0$ Notice in each case, as we reduce the second factor by 1, the product is being reduced by 3 So for consistency the next product in the pattern must be $0 - 3 = -3$
- Negative x Negative = Positive? Abstract Proofs – The Math . . .
There is a chain of reasoning -- a mathematical "argument" -- that shows why the rule *has* to be that negative times negative equals positive If someone did just decree this “rule”, then it would be annoying, wouldn’t it? But math is not about arbitrary rules; it’s about reasoning from basic assumptions or known facts, to less obvious facts
- 1. 5 Why is NEGATIVE TIMES NEGATIVE POSITIVE? - GDay Math
Positive times Negative: It does seem compelling to hold on to the “repeated addition” notion for the product of a negative and a positive: \(2\times \left(-3\right)=\) two groups of negative three \(=-3+-3=-6\)
- How to Explain Why a Negative Times a Negative is a Positive
A good way to explain why a negative times a negative is a positive is by means of pattern recognition Start with a sequence of multiplications, gradually introducing negative numbers Tell students to examine carefully the sequence of multiplication above for like 5 minutes
- Why Is Negative Times Negative Really Positive? - Medium
The reason why negative times negative is really positive is that our mathematical system requires it to be that way (logical consistency requirement)
- Why is a negative times a negative a positive? | Mathematical . . .
Those good reasons are mathematical: we want to make sure that when we extend multiplication and addition to negative numbers the properties of operations still apply In particular, we want the distributive property to apply Meditate on this: 3\cdot (5 + (-5)) = 3\cdot5 + 3 \cdot (-5)
- Why negative times a negative is positive - Mathematics for . . .
Among the ‘rules’ for working with negative numbers, the most counter intuitive is “negative times a negative is a positive” It is easily forgotten especially if it was learned by rote It is also not an easy ‘rule’ to make sense of so it needs to be learned with conceptual understanding
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