Explain why every integer is a rational number, but not all rational numbers are integers

A rational number, by definition, is a number that can be expressed as a quotient of two integers.

Every integer is a rational number because integers have an integer numerator and integer denominator (of 1).

For example, 3 is the same as 3/1.

3 can be expressed as a quotient of two integers, so it is a rational number.

Not all rational numbers are integers because of fractions. An integer would imply a result of a perfect division. Not all integers go evenly into each other.

Consider 4/2. This divides evenly to become 2.

But 1/2 is 0.5 in decimal form. 2 does not go evenly into 1.