5 -4 -3 -2 -1 0 1 2 3 4 5 6 -4 + 7 = 3 3 + (-4) = -7 4 + 3 = 7 3 + (-7) = -4 To which subset of real numbers does the following number belong? (1 point
- Which number sentence does the following number line represent? -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 -4 + 7 = 3 3 + (-4) = -7 4 + 3 = 7 3 + (-7) = -4 To which subset of real numbers does the following number belong? (1 point
The Correct Answer and Explanation is:
Correct Answer:
The number 3 belongs to the subset of whole numbers in the real number system.
Explanation:
The real number system is composed of several subsets, including natural numbers, whole numbers, integers, rational numbers, irrational numbers, and the overarching set of real numbers. Let’s analyze where the number 3 fits.
- Natural Numbers: These are the counting numbers starting from 1 (i.e., 1, 2, 3, 4, …). Since 3 is used for counting and is greater than zero, it is a natural number.
- Whole Numbers: These include all natural numbers plus zero. Therefore, the set is {0, 1, 2, 3, 4, …}. Since 3 is included in this set, it is a whole number.
- Integers: This set expands to include negative whole numbers, zero, and positive whole numbers (e.g., …, -3, -2, -1, 0, 1, 2, 3, …). Since 3 is within this set, it is an integer as well.
- Rational Numbers: These are numbers that can be expressed as the quotient of two integers (e.g., 3 = 3/1). So, 3 is a rational number.
- Irrational Numbers: These cannot be written as fractions (e.g., √2, π). 3 is not irrational.
- Real Numbers: This is the complete set that includes both rational and irrational numbers, so 3 is certainly a real number.
Among these, the smallest, most specific subset that includes 3 is the set of whole numbers.
Therefore, the correct subset of the real numbers to which 3 belongs is:
➡️ Whole Numbers.
