Tell which set or sets the number below belongs​ to: natural​ numbers, whole​ numbers, integers, rational​ numbers, irrational​ numbers, or real numbers.
four sevenths
4
7
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Part 1
Select all sets in which the number four sevenths
4
7 is an element.
A.
whole numbers
B.
real numbers
C.
irrational numbers
D.
natural numbers
E.
rational numbers
F.
integers

The number \(\frac{4}{7}\) belongs to the following sets:

- **B. Real numbers**: All numbers that can be represented on the number line, including both rational and irrational numbers, are real numbers. Since \(\frac{4}{7}\) can be represented on the number line, it is a real number.
  
- **E. Rational numbers**: Rational numbers are numbers that can be expressed as the quotient or fraction \(\frac{p}{q}\) of two integers, where \(p\) and \(q\) are integers and \(q \neq 0\). Since \(\frac{4}{7}\) is a fraction with integers in the numerator and denominator, it is a rational number.

\(\frac{4}{7}\) does not belong to the following sets:

- **A. Whole numbers**: Whole numbers are non-negative integers (0, 1, 2, 3, ...). \(\frac{4}{7}\) is not a whole number.
  
- **C. Irrational numbers**: Irrational numbers are numbers that cannot be expressed as a fraction of two integers. Since \(\frac{4}{7}\) is a fraction of two integers, it is not irrational.
  
- **D. Natural numbers**: Natural numbers are positive integers (1, 2, 3, ...). \(\frac{4}{7}\) is not a natural number.
  
- **F. Integers**: Integers include all whole numbers, both positive and negative, as well as zero (..., -2, -1, 0, 1, 2, ...). \(\frac{4}{7}\) is not an integer.

Thus, \(\frac{4}{7}\) belongs to sets **B. Real numbers** and **E. Rational numbers**.

Would you like more details on these sets or have any questions?

### Related Questions:
1. What is the difference between rational and irrational numbers?
2. Can you provide an example of an irrational number?
3. What makes a number an integer?
4. Why is \(\frac{4}{7}\) not a natural number?
5. How do natural numbers differ from whole numbers?
6. Can a real number be both rational and irrational?
7. What are examples of numbers that are not real?
8. How do you classify the number \(0\) in these sets?

**Tip:** Remember that all natural, whole, and integer numbers are also real numbers, but not all real numbers are natural, whole, or integer numbers.

Explore the concepts of number sets such as rational and real numbers. Learn why \(\frac{4}{7}\) belongs to the sets of real and rational numbers but not to whole, irrational, natural, or integer numbers. Suitable for Grades 6-8.

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