Answer:
The main difference between a fraction and a rational number lies in their definitions and scope.
Step-by-step explanation:
1. Fraction:
A fraction is a mathematical representation of a part of a whole. It consists of two parts: a numerator and a denominator. The numerator represents the number of parts we have, while the denominator represents the total number of equal parts in a whole. The numerator and denominator are separated by a fraction bar or a slash.
For example, in the fraction 3/4, the numerator is 3, indicating that we have three parts, and the denominator is 4, representing a whole divided into four equal parts.
Fractions can be proper (when the numerator is smaller than the denominator, e.g., 1/2) or improper (when the numerator is equal to or greater than the denominator, e.g., 5/4).
2. Rational Number:
A rational number is any number that can be expressed as a fraction, where the numerator and denominator are both integers. Rational numbers include whole numbers, integers, and fractions.
For example, 5 is a rational number because it can be written as 5/1, where the numerator is 5 and the denominator is 1. Similarly, 1/2 and -3/4 are rational numbers because they can be represented as fractions.
Rational numbers can be positive, negative, or zero, and they can be expressed in decimal form. Rational numbers can also be converted between fractions and decimals.
In summary, fractions are a specific representation of a part of a whole, while rational numbers encompass fractions as well as other types of numbers that can be expressed as fractions.