if p is an integer and q is a nonzero integer
If ( p ) is an integer and ( q ) is a nonzero integer, then the expression ( \frac{p}{q} ) will always yield a rational number. Additionally, since ( q ) is nonzero, ( p ) cannot be divided by zero, ensuring the division is valid. Furthermore, ( p + q ) will also be an integer, as the sum of two integers is always an integer.
Any fraction p/q where p is an integer and q is a non-zero integer is rational.
Then p/q is a rational number.
Yes, it is true that if ( p ) is an integer and ( q ) is a nonzero integer, then ( p ) can take any whole number value, including positive, negative, or zero, while ( q ) cannot be zero and must be a whole number either positive or negative. This distinction is important in mathematical contexts where division by zero is undefined.
Any fraction p/q where p is an integer and q is a non-zero integer is rational.
A rational number is any number of the form p/q where p and q are integers and q is not zero. If p and q are co=prime, then p/q will be rational but will not be an integer.
8 is an integer, which, by definition, are not irrational. In particular, an irrational number is a number that cannot be written in the form p/q for p and q both integers. However, since 8 clearly is equal to 8k/k for any integer k (and for that matter any nonzero number k), 8 is not irrational
The opposite of a nonzero integer is found by changing its sign. For example, if you have a nonzero integer like +5, its opposite is -5. This relationship holds for any nonzero integer; the opposite will always be the same number with an inverted sign. Thus, the opposite of a nonzero integer ( x ) is simply ( -x ).
A factor.
If: q = -12 and p/q = -3 Then: p = 36 because 36/-12 = -3
All integers {..., -2, -1, 0, 1, 2, ...} are rational numbers because they can be expressed as p/q where p and q are integers. Let p equal whatever the integer is and q equal 1. Then p/q = p/1 = p where p is any integer. Thus, all integers are rational numbers.
A rational number is always the result of dividing an integer when the divisor is nonzero.