Question

Is 55/22 a rational

Answer 1

The fraction
`\displaystyle (55)/(22)` is indeed a rational number.

Explanation:

A number
`x` is rational if and only if there exist two integers
`p` and
`q` (where
`q \\e 0`) such that
`x = \displaystyle (p)/(q)`.

`\displaystyle (55)/(22)`, the number in question here is already written in the form of a fraction. The two integers
`p = 55` and
`q = 22` (
`q \\e 0`) meet the requirement that
`\displaystyle (55)/(22) = (p)/(q)`. Therefore,
`\displaystyle (55)/(22)\!` is indeed a rational number.

Side note: the
`p` and
`q` here (
`q \\e 0`) don't have to be unique. For example:

because
`\displaystyle (55)/(22) = (5 * 11 )/(2 * 11) = \fraac{5}{2}`, both of the following pairs could satisfy
`\displaystyle (55)/(22) = (p)/(q)`:

• 
  `p = 55` and
  `q = 22`;
• 
  `p = 5` and
  `q = 2`.