What subsets of numbers does 8 2/3 belong to? Integers and real numbers Real and rational numbers Rational and natural numbers Whole and rational numbers
The correct answer and explanation is:
The correct answer is Real and Rational Numbers.
Let’s break down why that’s the case:
- Rational Numbers: A rational number is any number that can be expressed as the quotient of two integers, i.e., in the form ab\frac{a}{b}, where aa and bb are integers and b≠0b \neq 0. The number 8238 \frac{2}{3} can be written as 823=2638 \frac{2}{3} = \frac{26}{3}. Since this number is expressed as a fraction of two integers, it is classified as a rational number.
- Real Numbers: Real numbers include all rational and irrational numbers. They consist of all the numbers that can be found on the number line, including integers, fractions, decimals, and even irrational numbers like 2\sqrt{2}. Since rational numbers are a subset of real numbers, and 8238 \frac{2}{3} is rational, it is also a real number.
Let’s look at why the other choices are incorrect:
- Integers and Real Numbers: An integer is a number without a fractional part. While 8238 \frac{2}{3} is a real number, it is not an integer because of the fractional part 23\frac{2}{3}. Hence, it does not belong to the subset of integers.
- Rational and Natural Numbers: Natural numbers are the counting numbers starting from 1, 2, 3, and so on (sometimes including 0 depending on the definition). 8238 \frac{2}{3} is not a natural number because natural numbers do not have fractional parts, and 8238 \frac{2}{3} is a mixed number with a fraction.
- Whole and Rational Numbers: Whole numbers are non-negative integers (0, 1, 2, 3, …). Since 8238 \frac{2}{3} is not a whole number due to the fractional part, it does not belong to this subset.
Therefore, 8238 \frac{2}{3} belongs to the sets Real Numbers and Rational Numbers.