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When you take a negative fraction and write a rational number as a terminating decimal is the answer negative or positive?

- 126/35= -3.6


-9/24= -.379


Are these answers correct?  and what are the rules for dealing with negative fractions writing rational numbers as a terminating decimal?

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3 Answers

The sign (positive or negative) is completely independent of the magnitude of the fraction (or the repeating decimal) -- which means that you can ignore the signs when dividing, then decide whether it is postive or negative by counting how many minus signs there are in front of the numerator and denominator:  if the number of minus signs is ODD, then the number is negative; if even (including zero) minus signs preceed the value, then it is positive.

126 divided by 35 is 3+21/35 or 3+3/5 or 3.6; since there is one minus sign, the answer is -3.6

9 divided by 24 is 9/24 or 3/8 or .375; since there is one minus sign, the answer is -0.375

(-.379 is incorrect).


To check equality between a fraction and a number with a decimal you can divide the numerator by the denominator. The fact that it is a negative will not change by doing this.


-126 divided by 35 equals -3.6.


-9 divided by 24 equals -.375.


So, as far as I can see, the first one is right but the second one is wrong.

Bruce and Chris are both correct, but to simplfy things a bit...whenever you mix a negative and a positive number together, by multiplication or division, you ALWAY get a negative number.  So 3 times -5 is -15 and -20 divided by 10 is -2.  Two positive numbers always stay positive and two negative numbers become positive so 10 times 10 is 100 and -5 times -5 is 25 and -30 divided by -5 is 6.  That the answers to your questions are not whole numbers makes no difference.  You are dividing -126 by 35 (or 126 by -35, makes no difference) and you get -3.6