Subjects number theory

Classify Negative Nine 7A523A

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1. **State the problem:** We need to determine which classifications apply to the number $-9$ from the options: rational number, real number, whole number, and integer. 2. **Recall definitions:** - A **rational number** is any number that can be expressed as $\frac{p}{q}$ where $p$ and $q$ are integers and $q \neq 0$. - A **real number** includes all rational and irrational numbers. - A **whole number** is a non-negative integer (i.e., $0,1,2,3,\dots$). - An **integer** is any whole number or its negative counterpart (i.e., $\dots,-3,-2,-1,0,1,2,3,\dots$). 3. **Check $-9$ against each definition:** - $-9$ can be written as $\frac{-9}{1}$, so it is a rational number. - $-9$ is a real number because all rational numbers are real. - $-9$ is not a whole number because whole numbers are non-negative. - $-9$ is an integer because it is a negative whole number. 4. **Conclusion:** $-9$ is a rational number, a real number, and an integer, but not a whole number. **Final answer:** $-9$ is a rational number, real number, and integer.