Question 199626
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If you are using the asterisk (*) to indicate division, you are really confusing the issue.  The asterisk generally denotes multiplication.  But here are the rules.


Let *[tex \Large a] and *[tex \Large b] represent numbers greater than zero, that is positive numbers.  That means that *[tex \Large -a] and *[tex \Large -b] are negative numbers.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ a \times b = ab]; a positive number


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ -a \times b = -ab]; a negative number


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ a \times -b = -ab]; a negative number


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ -a \times -b = ab]; a positive number


Now, as to division:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ a \div b = \frac{a}{b}] is the same thing as:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ a \times \frac{1}{b}]


In other words, division is nothing more than multiplication by the reciprocal (the reciprocal is simply turning the fraction upside down, *[tex \Large a = \frac{a}{1}] so the reciprocal is *[tex \Large \frac{1}{a}])


Therefore you can use the same rules for division that you use for multiplication.  In simple, easy to remember terms:


<b><i>If the signs are the same, the result is positive.


If the signs are different, the result is negative.</i></b>


For the problem you indicated as -6*-4, which I would have otherwise interpreted as minus 6 times minus 4 = positive 24, that you seem to indicate means minus 6 divided by minus 4, yes, if you are doing integer division then the quotient is 1.  However the remainder is -2, (<i>the remainder always has the sign of the divisor regardless of the sign of the dividend</i>) but ordinary division would say:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ -6 \div -4 = \frac{-6}{-4} = \frac{3}{2} = 1\frac{1}{2} = 1.5]


If your -8*-16 actually means minus 8 divided by minus 16, then -16 goes into -8 zero times, so the quotient is zero with a remainder of -8 in the case of integer division, whereas:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ -8 \div -16 = \frac{-8}{-16} = \frac{1}{2} = 0.5]


I'm less than absolutely certain, but I have a strong sense that your course work at Embry Riddle Aeronautical will seldom, if ever, require you to perform integer division, rather, you will be expected in most cases to provide decimal representations of your quotients, whether they be exact or approximations.


Good luck.



John
*[tex \LARGE e^{i\pi} + 1 = 0]
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