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.