Q: Why does the sign change when multiplying and dividing negative numbers?

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because of mathematical equivalence: it doesn't change the result

show how to solve -2X-4<10 -2X<14 X>-7 (you must change the sign when multiplying or dividing by negatives) Not sure what show steps of how to solve- 10 of 90 means

a car braking is a negative rate of velocity change

Rise/run or y-value change (can be negative) / x-value change (can be negative)

Flip the fraction around (the one after the division sign) and change it to a multiplication sign. (swap the numerator with the denominator) so 2/(3/10) = 2*(10/3) The reason you do so is if you think of multiplication and dividing revolving around the number 1, in multiplying if you are above 1 then you are increasing if you are lower you are increasing. The opposite is the same of division. Effectively, if you think about it multiplication is the inverse of division and the other way around as well, so by flipping the fraction you are inverting it, so instead of dividing by 0.5 you multiply by 2. I hope this makes sense, it could be shown algebraically, but it is probably easier to understand this way.

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Multiplying and dividing integers is real easy. All you have to do is do regular dividing and multiplying keeping in mind these simple rules: RULES: 1: When multiplying or dividing integers, when the numbers are a positive, positive they equal a positive. When the numbers are negative, negative they equal a positive. In other words, same signs equal positive. 2: This rule is very similar to the rule above. The only change is that when the signs are different, they equal a negative. ( negative, positive= negative, positive, negative= negative.) Please correct me if I'm wrong. Multiply integers- my notes from class positive x positive= positive positive x negative= negative negative x negative= positive Divide integers- again my notes from class positive divided by a positive= positive negative divided by a negative= positive negative divided by a positive= negative Dividing integers are simple if the number has a different sign than the other it is always negative but if they have the same sign its always positive ex. -20/5=-4 ex. -20/-4=-5

Multiplying something by a negative number makes it change signs. A positive number multiplied by a negative is negative therefore a negative * a negative is positive.

because of mathematical equivalence: it doesn't change the result

123.456 is changed into fraction by multiplying and dividing it by a number such that both denominator and numerator don't contain decimal. Multiplying and dividing by 100, we get 123.456 as 123456/100.

Adding integers, if they have the same sign, add their absolute values and keep the same sign. Subtracting, change the sign of the 2nd number and the add using rules of addition. Multiplying and dividing, Divide the absolute values, if the signs are the same the answer is positive, if the signs are different the answer is negative.

Adding or subtracting zero cant, multiplying or dividing by zero can.

No, multiplying or dividing mass and volume by the same factor will not affect density because density is calculated by dividing mass by volume. As long as the mass-to-volume ratio remains constant, the density will not change.

Because common denominators allow adding and subtracting of numerators. Improper fractions also have simplified rules over mixed numbers when performing multiplication and division.

You don't.

Numbers are justified as positive, which is usually written as just a number but can be written with a plus (+) sign in front of the number. (e.g. 15 or +15), or negative. Negative numbers are numbers in the negative integers, or below 0. They are written with a minus (-) sign in front of them. (e.g. -15) ---------------------------------------------------------------------------------- ..::To solve remember these rules::.. When multiplying: positive x negative = negative positive x positive = positive negative x negative = positive When dividing: positive / negative = negative positive / positive = positive negative / negative = positive When adding: In a positive + negative situation, if the negative number has a higher number than the positive (e.g. -25 + 10) then the number is negative, this is always true when adding a higher negative to a positive. If the positive has a higher number (e.g. 25 + -10) then it's just the opposite, it will be a positive number. -------------You can solve these very easily: 25 + -10 --> (25) + (-10) to keep it well organized and easier to work with,now just remember "Keep Change Change"... - keep 25 as it is, change "+" to a "-" and change the "-10" to a positive 10. As a result, you will have: 25 - 10. Now solve. Answer = 15 (positive). If for instance you have a negative + positive, the same rules apply (Keep Change Change) negative + negative = negative positive + positive = positive When subtracting: negative - positive (vice versa), use Keep Change Change as you did with adding positives and negatives. negative - negative, use Keep Change Change positive - positive, use Keep Change Change if the number you are subtracting is a higher number. (e.g. 10-15) If you need anymore help, try asking a more specific question again on Wikianswers, search for math websites on the web, or ask your teacher or college professor for help.

No. The commutative and associative laws are valid for any real numbers.

the inequality sign will only change in an equation if you are multiplying or dividing by a negative number... for example if you have the equation -1x+2>3 you would subtract by 2 you would have -1x>1 the next step is -1x>1 -1 -1 your dividing by -1 so the sign flips from greater than to less than (it can go less than to greater than too) and your final answer would be x<-1