Portal talk:Mathematics/FAQ

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arithmatic -x- =+

arithmatic is quite a simple form of mathematics which is easy to understand and seem to have certain easy rules like 1.1 x 1.1 wil be more than 1.1 and .9 x .9 will be less than .9 most can see why but this can dedemonstrated. Then how does a minus times a minus make plus figure is there any demonstrable example of this. or is it just the case that it can not be easily demontated so its deemed to be the case. regards paul

This question has been unanswered for some time, perhaps because the questioner seems challenged by the English language. However, it's an insightful, common, and fun question, deserving a brief response. Before arithmetic there was counting: 1, 2, 3, … . Each of these natural numbers has a successor, a number that is one larger. If we count two piles of stones separately, then bring them together and count again, we discover the operation of addition. We can formally define addition by repeatedly taking successors. Similarly, we can formally define multiplication by repeated addition. Using stones, we can form multiples by lining up rows and columns. In both our formal methods and our physical methods we notice certain reliable patterns, certain facts which are always true regardless of the specific numbers involved. One of these facts is that multiplication distributes over addition. For example, we know that 5 = 2+3, and we know that 20 = 4×5; distribution means we can expect that 4×5 = 4×(2+3) = 4×2+4×3. And, indeed, 8 = 4×2, 12 = 4×3, and 20 = 8+12. Pictured in stones, this is obvious:

* * * * *         * * *   * *
* * * * *         * * *   * *
* * * * *    =    * * *   * *
* * * * *         * * *   * *

From these humble beginnings we extend our operations to do more sophisticated calculations. We subtract and divide, take powers and square roots, and with our ancient ancestors in Babylon and Egypt learn to do trigonometry with sines and cosines and tangents. To keep up, our numbers grow to include zero and fractions and negative numbers. But we still expect our familiar patterns to hold. So consider the multiplication 4×5 again, but now use subtraction to write 4 = 7−3 and 5 = 6−1. The way negative numbers relate to subtraction allows us to also write 4 = 7+(−3) and 5 = 6+(−1). Now what happens when we multiply these sums? Play with stones (removing rows and columns to subtract), or play with distribution and find out! For example, the picture above can also explain 4×3 = 4×(5−2). By such experiments or calculations, we discover that the only way to get the answers we expect is to make negative times negative equal positive. If this still seems peculiar, take solace in knowing that for thousands of years mathematicians in the Western world did not accept negative numbers as numbers, and accountants still use debits and credits and red ink to avoid them. --KSmrq^T 11:16, 13 October 2005 (UTC)[reply]

My own version why minus times minus is plus... imagine it isn't i.e. -1 * -1 = -1 --> -1 * -1 / -1 = -1 */-1 --> -1 * (-1 / -1) = (-1 / -1) --> -1 * 1 = 1 --> -1 = 1, which clearly isn't true. Hence it can't be true that that -1 * -1 = -1 . Tompw 17:28, 4 December 2005 (UTC)[reply]

Factor the following

1:b^-3/5-7b^-2/5+2b^2/5

2:3(x+3)^-1/3+2(x+3)^4/3

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