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

Arational 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.

Ibelieve the answer would be 7, 13, 23