Question

check each set that includes the number shown.
$\frac{5}{9}$
natural numbers
whole numbers
integers
rational numbers
irrational numbers
real numbers

Explanation:

Step1: Define number sets

Natural numbers are positive whole - numbers starting from 1 ($1, 2, 3,\cdots$). Whole numbers are non - negative integers ($0, 1, 2,\cdots$). Integers are whole numbers and their negatives ($\cdots,- 2,-1,0,1,2,\cdots$). Rational numbers are numbers that can be written as $\frac{a}{b}$ where $a$ and $b$ are integers and $b
eq0$. Irrational numbers cannot be written as a fraction. Real numbers include both rational and irrational numbers.

Step2: Analyze $\frac{5}{9}$

Since $\frac{5}{9}$ is a fraction where 5 and 9 are integers and $9
eq0$, it is a rational number. It is not a natural number (not a positive whole number starting from 1), not a whole number (not an integer), not an integer, and not an irrational number. Since it is rational, it is also a real number.

Answer:

rational numbers, real numbers