Name the set or sets of numbers to which each real number belongs.

$\frac{36}{6}$

Real numbers include all the numbers except complex numbers and have the following five subsets:

1. Natural numbers: Includes counting objects and start from 1.
2. Whole numbers: Includes the set of natural numbers along with 0.
3. Integers: Z = Includes numbers that are not fraction (positive and negative whole numbers)
4. Rational numbers: Includes the numbers which can be written in the form of $\frac{p}{q}$where p and q are integers, $q\ne 0$.
5. Irrational numbers: Includes numbers that cannot be written in the form of $\frac{p}{q}$where p and q are integers,$q\ne 0$.

1. Natural numbers: $\left\{1,2,3,4,...\right\}$

2. Whole numbers:$\left\{0,1,2,3,4,...\right\}$

3. Integers: Measurement of debts, temperatures, etc., fall under the set of integers $\left\{...,-3,-2,-1,0,1,2,3,...\right\}$

4. Rational numbers: If we cut a cake into equal pieces, then we may have a piece that represents a fraction like$\frac{5}{6},1.5\left(=\frac{3}{2}\right),\frac{6}{9},\frac{8}{3}$

5. Irrational numbers: The numbers that are square roots of positive rational numbers, cube roots of rational numbers, etc., such as$\sqrt{2},\sqrt[3]{5},-\sqrt{3}$

Consider the given real number$\frac{36}{6}$

We can rewrite it as:

$$\begin{gathered} \frac{36}{6}=\frac{6\times 6}{6} \\ =6 \\ =\frac{6}{1} \end{gathered}$$

Now we will check each subset of real numbers:

1. Natural numbers: They are positive, countable and start from 1. So, $\frac{36}{6}=6$being positive, countable and greater than 1 is a natural number.
2. Whole numbers: They are natural numbers including 0. So,$\frac{36}{6}=6$ being a natural number is a whole number as well.
3. Integers: They are whole numbers that are both positive and negative. So,$\frac{36}{6}=6$ being a whole number is an integer as well.
4. Rational numbers: They can be written in the form $\frac{p}{q}$where p and q are integers, $q\ne 0$. Since,$\frac{36}{6}=6$ it is a rational number.
5. Irrational numbers: They cannot be written in the form $\frac{p}{q}$where p and q are integers, $q\ne 0$. Since from the above point,$\frac{36}{6}$ can be written in the form role="math" localid="1641498934115" $\frac{p}{q}$, it is not an irrational number.

Therefore, the real number $\frac{36}{6}$belongs to the set natural numbers, whole numbers, integers and real rational numbers.