A rational number is any number that can be expressed as a fraction, where the numerator is an integer and the denominator is a non-zero integer. So, both rational numbers that are integers and those that are not integers fall under this definition. The main difference lies in their value and representation.
An integer is a whole number that can be positive, negative, or zero, such as -3, 0, and 5. When we say a rational number is an integer, we mean it can be represented as a fraction with the denominator of 1, like 5 can be written as 5/1.
On the other hand, a rational number that is not an integer can be fractions that don’t simplify to whole numbers, like 1/2 or -3/4. These numbers cannot be represented as whole numbers because they lie between integers on the number line.
In summary, while all integers are rational numbers, not all rational numbers are integers. Integers are specific types of rational numbers with no fractional part, whereas rational numbers that are not integers contain a fractional component.