# why is -4 a rational number [closed]

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_addictedOct 26 '17 at 6:13

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Community, Lord Shark the Unknown, Krish, Shailesh, choco_addicted
If this question can be reworded to fit the rules in the help center, please edit the question.

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

## 3 Answers

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.