Question

What is the set of numbers to which \[\dfrac{56}{7}\]belong?

Answer 1

Hint: In the above type of question we are asked to find the to what set of numbers does the given term belongs to, for that first we are going to learn how many different sets of number are there and based on the theories we can check on which set does the term belong.

Complete step by step solution:
For the above type of question: first we are going to learn about what different sets are there:
There are many different sets of numbers such as: Integer, real, whole, rational, natural and irrational. Now let us understand what these sets of numbers signify and how we can identify them. Integer is a type of number which has no fractional part in it for example 9.2, 8.75, \[4\dfrac{2}{3}\], and also these numbers do not include zero (0). In short, integers are numbers which can take up values from \[-\infty \] to \[\infty \] excluding zero and all fraction values whereas when we look at whole numbers these are also integers which include zero (0). In short whole numbers are sets of numbers which take every single number between \[-\infty \] to \[\infty \] including zero but excluding fractions. Real numbers are sets of numbers which take every number from \[-\infty \] to \[\infty \] including zero and fraction. In short any number which can be plotted in a number line is a real number. Rational numbers are a set of numbers in which the fractions have a terminating end whereas in irrational numbers there is no ending for example\[\sqrt{2},\sqrt{3}\].
Now in the question that has been mentioned to us when we simplify it we will get a value i.e.
\[\dfrac{56}{7}=8\]
Now we can clearly see that 8 is an integer, a whole number, a rational number, a natural number and a real number.

So finally we can define the fraction given to us to be an integer, a whole number, a natural number, a real number and a rational number

Note: In these types of questions when we have been asked about a term and mention that term in what type those numbers belong to we will define all the sets to why it belongs and why it does not belong to that set of numbers.