Question

3 samantha is reviewing her math notes on number classifications. she writes the following examples: chart with number and classifications: 12 - rational number, integer, whole number, natural number; -5 - rational number, integer; 0 - rational number, integer, whole number; -8.25 - rational number which statement best explains why -5 is classified as a rational number? (a) all integers are rational numbers because they can be written as a ratio of two integers. (b) all integers are irrational numbers because they are not fractions. (c) all integers are natural numbers, and natural numbers are rational. (d) all integers are whole numbers, and whole numbers are rational.

Explanation:

To determine why -5 is a rational number, we analyze each option:

• Option A: A rational number is defined as a number that can be expressed as $\frac{p}{q}$ where $p$ and $q$ are integers and $q

eq0$. Integers (like -5) can be written as $\frac{-5}{1}$ (ratio of two integers), so this is correct.

• Option B: Integers are not irrational. Irrational numbers can't be expressed as a ratio of two integers, but integers can (e.g., $\frac{-5}{1}$), so B is wrong.
• Option C: Not all integers are natural numbers (natural numbers are positive integers, so -5 is not a natural number), so C is wrong.
• Option D: Not all integers are whole numbers (whole numbers are non - negative integers, so -5 is not a whole number), so D is wrong.

Answer:

A. All integers are rational numbers because they can be written as a ratio of two integers.