to which subsets of real numbers does the number -22 belong? choose all that apply
a) whole numbers
b) rational numbers
c) integers
d) irrational numbers
e) natural numbers
rationals and integers
To determine which subsets of real numbers the number -22 belongs to, let's go through each option:
a) Whole numbers: Whole numbers are non-negative integers (0, 1, 2, 3, ...). Since -22 is a negative number, it does not belong to the set of whole numbers.
b) Rational numbers: Rational numbers are numbers that can be expressed as a fraction of two integers. -22 can be written as -22/1, so it is a rational number. Therefore, -22 belongs to the set of rational numbers.
c) Integers: Integers include all positive and negative whole numbers, including zero. Since -22 is a negative whole number, it belongs to the set of integers.
d) Irrational numbers: Irrational numbers cannot be expressed as a fraction of two integers. Examples of irrational numbers include the square root of 2 and pi. -22 is a rational number, not an irrational number. Therefore, -22 does not belong to the set of irrational numbers.
e) Natural numbers: Natural numbers are positive whole numbers (1, 2, 3, ...). Since -22 is a negative number, it does not belong to the set of natural numbers.
In summary, the number -22 belongs to the subsets of real numbers: rational numbers and integers (options b and c).
To determine which subsets of real numbers the number -22 belongs to, we can examine the definitions of each subset and evaluate whether -22 meets the criteria.
a) Whole numbers include all positive numbers, zero, and negative numbers without any fractions or decimals. Since -22 is a negative number without any fractions or decimals, it is a whole number. Thus, -22 belongs to this subset.
b) Rational numbers include all numbers that can be expressed as a fraction p/q, where p and q are integers (whole numbers) and q is not equal to 0. Since -22 can be written as -22/1, with p = -22 and q = 1 being integers and q ≠ 0, -22 is a rational number. Thus, -22 belongs to this subset.
c) Integers include all positive numbers, zero, and negative numbers without any fractions or decimals. Since -22 is a negative number without any fractions or decimals, it is an integer. Thus, -22 belongs to this subset.
d) Irrational numbers include all numbers that cannot be expressed as a fraction p/q, where p and q are integers (whole numbers) and q is not equal to 0. Since -22 can be expressed as -22/1, where p = -22 and q = 1 are integers and q ≠ 0, -22 is not an irrational number. Thus, -22 does not belong to this subset.
e) Natural numbers include all positive numbers excluding zero. Since -22 is a negative number, it is not a natural number. Thus, -22 does not belong to this subset.
Therefore, the subsets of real numbers to which -22 belongs are a) whole numbers, b) rational numbers, and c) integers.