# 12.4 Comparisons of Rationals

`q1 = q2`
`q1 < q2`

The equality operator `=` evaluates to `true` if the two rationals q1 and q2 are equal and to `false` otherwise. The inequality operator `<` evaluates to `true` if the two rationals q1 and q2 are not equal and to `false` otherwise.

```    gap> 2/3 = -4/-6;
true
gap> 66/123 <> 22/41;
false
gap> 17/13 = 11;
false ```

`q1 < q2`
`q1 <= q2`
`q1 q2`
`q1 = q2`

The operators `<`, `<=`, , and `=` evaluate to `true` if the rational q1 is less than, less than or equal to, greater than, and greater than or equal to the rational q2 and to `false` otherwise.

One rational q_1 = n_1/d_1 is less than another q_2 = n_2/d_2 if and only if n_1 d_2 < n_2 d_2. This definition is of course only valid because the denominator of rationals is always defined to be positive. This definition also extends to the comparison of rationals with integers, which are interpreted as rationals with denominator 1. Rationals can also be compared with objects of other types. They are smaller than objects of any other type by definition.

```    gap> 2/3 < 22/41;
false
gap> -17/13 < 11;
true ```

GAP 3.4.4
April 1997