Question

Which of these are rational numbers: `\frac { 7} { 6} ,11,- \frac { 1} { 4}, -5.4`?

Answer 1

All of them

Explanation:

A rational number is any real number that can be expressed as: `p/q {p,q } in ZZ: q!=0`
I.e the ratio of two integers. We need to state that `q` cannot be `0` as division by `0` is undefined.

Rational numbers are said to be `in QQ`

Taking each example in this question in turn.

`7/6`: `{7, 6} in ZZ -> 7/6 in QQ`

`11 = 11/1: {11,1} in ZZ -> 11 in QQ` [NB: 11 is, of course, also `in ZZ`]

`-1/4 = (-1)/4 or 1/(-4): {-1, 4, 1, -4} in ZZ -> -1/4 in QQ`

`-5.4 = (-54)/10: {-54, 10}in ZZ -> -5.4 in QQ`