any number that can be represented as the ratio of two integers

And the simple way to think about the simple way is any number that can be represented as the ratio of two integers is a rational number.

a number that can be written as a fraction of two integers

Under rational numbers, the second sentence should read 'Any number that can be written as a fraction of two integers is a rational number.'

Any number that can be shown as a fraction

Any number that can be shown as a fraction is by definition a rational number.

the quotient of two integers

The definition of a rational number is the quotient of two integers (as long as the denominator is not a zero).

a number in which the denominator and numerator are both integers (except, the denominator can't be zero)

A rational number is a number in which the denominator and numerator are both integers (except, the denominator can't be zero).

A number which can be expressed as pq, where p and q are integers and q≠0

A number which can be expressed as pq, where p and q are integers and q≠0 is a rational number.

a number of the form a/b

Rational number is a number of the form a/b, where a and b are integers, and b is not equal to zero.

The quotient of a positive integer and a negative integer

The quotient of a positive integer and a negative integer is a rational number.

the number of the form where p and q are integers

A rational number is the number of the form where p and q are integers.

Any number that can be rewritten as a simple fraction

Any number that can be rewritten as a simple fraction is a rational number.

a real number

A rational number is a real number that can be written as a ratio of two integers.

a number that can be expressed in the form of p/q

A rational number is a number that can be expressed in the form of p/q.

any number that can be written as a fraction, where both the top number (numerator) and the bottom number (denominator) are integers

A rational number is any number that can be written as a fraction, where both the top number (numerator) and the bottom number (denominator) are integers.

The product of two irrational numbers

Thus, the product of two irrational numbers is a rational number.

Integers

Integers are rational numbers because they can be written as fraction with 1 as the denominator.

any number ,, that can be written in fraction formwhere a and b are integers and b ≠ 0 

A rational number is any number that can be written in fraction form,, where a and b are integers and b ≠ 0 

any real number that can be Irrational numbers

A rational number is any real number that can be Irrational numbers

The number x

Now, ~p: The number x is a rational number.

The quotient of a division

The quotient of a division of one rational number by a non-zero rational number is a rational number.

a subset of the number system

A rational number is a subset of the number system.