Yes, fractions are rational numbers.
A rational number is any number that can be expressed as the quotient or fraction p/q of two integers, where p is the numerator and q is the denominator, and q is not equal to zero. Since a fraction is, by definition, expressed as a numerator divided by a denominator (with the denominator not being zero), it perfectly fits the definition of a rational number.
For example:
- 1/2 is a rational number and a fraction.
- -3/4 is a rational number and a fraction.
- 5/1 is a rational number and a fraction (which can be simplified to the integer 5).
It's important to note, however, that while all fractions are rational numbers, not all rational numbers are always written as fractions in their simplest form. Integers, for example, are rational numbers because they can be expressed as a fraction with a denominator of 1 (e.g., 5 = 5/1), but we typically don't write them as fractions. Similarly, some decimals that terminate or repeat can also be expressed as fractions, therefore they are rational numbers (e.g., 0.5 = 1/2).
In summary, the set of fractions is a subset of the set of rational numbers. All fractions are rational numbers, because they meet the requirement of being expressible in the form p/q, where p and q are integers and q is not zero.
