Describe the relationship between whole numbers, integers, and rational numbers.
Whole numbers are a subset of integers and integers are a subset of rational numbers.
Whole numbers consist of the set of natural numbers (or counting numbers) as well as zero (0). This means that whole numbers include numbers like 0, 1, 2, 3, 4, and so on. Whole numbers only represent positive values or zero and do not include any fractions or decimals.
Integers, on the other hand, include both positive and negative whole numbers as well as zero. The set of integers includes numbers like -3, -2, -1, 0, 1, 2, 3, and so on. Integers are formed by adding negative counterparts to whole numbers and can represent values that are both positive and negative.
Rational numbers encompass integers along with any number that can be expressed as a fraction of two integers. Rational numbers include numbers like 1/2, 3/4, -5/6, 2, -3, and so on. Rational numbers can represent values that are positive, negative, or zero, and they can be expressed as fractions or decimals.
In summary, the relationship between whole numbers, integers, and rational numbers is that whole numbers are a subset of integers, and integers are a subset of rational numbers.
The relationship between whole numbers, integers, and rational numbers can be understood as follows:
1. Whole numbers: Whole numbers are a set of numbers that includes all the positive integers (0, 1, 2, 3, ...), without any fractions or decimals. Whole numbers are closed under addition and multiplication.
2. Integers: Integers are a set of numbers that includes whole numbers and their additive inverses (negatives). In other words, integers consist of all the positive and negative whole numbers along with zero (..., -3, -2, -1, 0, 1, 2, 3, ...). Integers are also closed under addition and multiplication.
3. Rational numbers: Rational numbers are a set of numbers that can be expressed as a fraction, where both the numerator and the denominator are integers. The numerator can be positive, negative, or zero, but the denominator must be nonzero. Rational numbers include integers because every integer can be expressed as a fraction by setting the denominator to 1. For example, 3 can be expressed as 3/1. Rational numbers are closed under addition, subtraction, multiplication, and division (except division by zero).
In summary, rational numbers include both integers and, as the name suggests, all the numbers that can be expressed as a ratio or fraction. So, the relationship can be represented as:
Whole numbers ⊂ Integers ⊂ Rational numbers
Whole numbers, integers, and rational numbers are all different types of numbers that are related to each other in the realm of mathematics.
First, let's start with whole numbers. Whole numbers are the set of numbers that includes all the positive numbers (1, 2, 3, ...) and zero (0) but excludes negative numbers. These numbers are used to count or represent quantities that are not divided into fractions or decimals.
Next, we have integers. Integers include all the whole numbers (0, 1, 2, 3, ...) and their negative counterparts (-1, -2, -3, ...). In other words, integers are the set of all whole numbers along with their negatives.
Finally, rational numbers encompass a wider range of numbers. A rational number is any number that can be expressed as a fraction, where the numerator and denominator are integers. This includes whole numbers and integers, as they can be expressed as fractions with a denominator of 1, but it also includes numbers like 1/2, -3/4, 0.75, etc. In other words, rational numbers are numbers that can be written in the form "a/b" where "a" and "b" are integers.
To summarize, whole numbers are a subset of integers, and integers are a subset of rational numbers. While whole numbers and integers are limited to positive and/or negative whole numbers, rational numbers extend beyond that to include fractions and decimals that can be expressed as ratios of integers.