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From Algebra $1$ For Dummies:

Multiplying and dividing numbers with signs Multiplication and division are by far the easiest operations to do with the signs. As long as you can multiply and divide, the rules are simple and are exactly the same for both operations. When multiplying and dividing two numbers with signs: if the two signs are equal, the result is positive; when the two signs are different, the result is negative.

$(+a) × (+b) = + ab$

$(+a) × (-b) = -ab$

$(-a) × (+b) = -ab$

$(-a) × (-b) = + ab$

$(+a)÷(+b) = +(a÷ b)$

$(+a) ÷ (-b) = -(a÷b)$

$(-a)÷(+b) = -(a÷b)$

$(-a) ÷ (-b) = + (a÷b)$

Note in which cases the answer is positive and in which cases it is negative. Note also that multiplication and division appear the same as always, except for positive and negative signs. See the examples below:

$(-8) × (+2) =-16$

$(-5) × (-11) = +55$

$(+24)÷(-3)= -8$

$(-30)÷ (-2)=+15$

"Except for the positive and negative signs?" I don't notice the difference..

Mathemagician314
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Gui
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    I would probably say "ignoring the positive and the negative signs" rather than "except for..." . My guess is that the author is expecting that the reader is familiar with multiplication of unsigned numbers ("as always", say $8\times 2=16$) and all they want to say is that you can ignore the sign at first, to calculate the unsigned result ("same as always") and then just change the sign (or not) according to those (presumably new to the reader at this point) rules. So, $(-8)\times (+2)$ is one of $\pm\color{red}{16}$ and cannot be anything else. –  Nov 20 '22 at 19:44
  • . So, (−8)×(+2) is one of ±16 and cannot be anything else.Can’t understand – Gui Nov 20 '22 at 19:50
  • And then, you only need to check if it is going to be $+16$ or $-16$, so you follow the rule "when two signs are different, the result is negative". $-2$ and $+8$ have different signs, so the result is $-16$. –  Nov 20 '22 at 19:54
  • Basically, use your times tables to calculate the result up to the sign, and use these new rules (about the sign) to figure out the sign. –  Nov 20 '22 at 19:56

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