I need to know why -4 is a rational I am very confused. I am doing my homework and have been stuck on this question the whole time I thought that it would be a intger.

edit:thanks for the help


closed as off-topic by user99914, Lord Shark the Unknown, Krish, Shailesh, choco_addicted Oct 26 '17 at 6:13

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  • 2
    $\begingroup$ Is an apple a fruit? $\endgroup$ – Thomas Andrews Oct 26 '17 at 2:30
  • $\begingroup$ Every integer is a rational number. $\endgroup$ – Lubin Oct 26 '17 at 2:31
  • $\begingroup$ If this is an apple, how can it also be a fruit? $\endgroup$ – Thomas Andrews Oct 26 '17 at 2:31
  • $\begingroup$ $\mathbb{Q}=\{\frac{p}{q}|p\in\mathbb{Z}, q\in\mathbb{N}_{>0}\}$. Do you find such a notation for $-4$? Which? $\endgroup$ – Cornman Oct 26 '17 at 2:32
  • $\begingroup$ $-4=\frac{-4}{1}$, ie is representable by $\frac{a}{b}$ where $b \ne 0$ and $a$ and $b$ are integers. $\endgroup$ – Travis Oct 26 '17 at 2:44

A number is rational if it can be expressed as the ratio of two integers, which $-4$ can: $\frac{-4}{1}$. It is also an integer; the set of integers is a subset of the set of rational numbers.


$-4 = \frac{-4}{1}$, that is to say, it can be represented as a ratio in the form $\frac{a}{b}$ where $b \ne 0$ and $a$ and $b$ are integers. This is the definition of a rational number.

$-4$ is also an integer, and integers are a subset of rational numbers.


The set of all integers are in the set of rationals. Just like how the set of all naturals are in set of integers.


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