Iff a/b is a rational number, what does b have to equal in order for a/b to also be an integer

You're thinking b=1 will always give an integer, certainly true.

Then you think b=-1 will also always give an integer, so

Answer: ±1

Then you remember that a/b may not be a reduced fraction, so other bs beside the unit make give integers. The condition for an integer is

b | a

read 'b divides a' meaning a is a multiple of b.

Then you realize that a and b might not even b integers themselves.

Let's say the above answer is correct with the additional criteria that a and b are integers with no common factors.

Answer: b must equal a.

Or b must equal a multiple of the reciprocal of "a" if "a" is an integer.

Or "b" is a fraction with the numerator equal to "a" or a multiple of "a." If "a" is an integer

Step-by-step explanation:

Integers are whole numbers. If the denominator of the fraction is equal to the numerator, the value is 1 which is an integer.

If a is divided by its reciprocal the quotient is a whole number. For example: 3: 1/3 = 9. 4: 1/8 = 32.

If b is a fraction that is not a multiple of the reciprocal, the quotient may be another non-intrger rational number. 3: 4/5 is 15/4 or 3 3/4.

7: 7/8 is 56/7 which is equivalent to 8, an integer.