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In math, sometimes I see a negative symbol beside the fraction bar. Does that mean both the numerator and the denominator are negative, or just the numerator?

saucymathematician
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  • The negative symbol applies to the result of the fraction division. It is equivalent to the multiplication of the fraction by -1. If you want, you can consider the negative in either the numerator or the denominator but not in both. – user144410 Nov 06 '18 at 21:52
  • Are you concerned only with fractions in which both the numerator and denominator are explicitly named integers, such as $-\frac 23,$ or does this question concern any time you have a negative sign in front of a fraction bar, for example in an expression with unknowns like $-\frac xy$? – David K Nov 06 '18 at 22:04

3 Answers3

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No, it means the whole fraction is negative. So $$-\frac 12=-\left(\frac 12\right)$$ Both the $1$ and the $2$ are positive, then we apply the negative sign to the whole thing.

Ross Millikan
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Elaborating a bit on the previous answer, that the whole fraction is negative means that the numerator and the denominator have opposing signs. It doesn't matter which is positive and which is negative

$$ -\frac{1}{2}=\frac{-1}{2}=\frac{1}{-2}$$

Patricio
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The negative sign in front of the bar could by multiplied by the top or the bottom but not both.

For example $$-\frac {3}{5} = \frac {-3}{5} = \frac {3}{-5}$$

or $$ -\frac {-2}{7} = \frac {2}{7} $$

or $$ - \frac {5}{-6} =\frac {5}{6} $$

Mohammad Riazi-Kermani
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  • if $-\frac{a}{b}:=:\frac{-a}{b}$ then why $-\frac{a}{b}-\frac{c}{b}$ is not equal to $-\frac{a-c}{b}$ ? having a hard time getting my head around that, its like when adding negative fraction you have to put the sign to the numerator, other ways turns in inequality? – bau8312 Feb 23 '22 at 08:31