Question

Which fraction is less than 1 chose all of the correct answer, and explain why you chose and write it down and explain your answer. 7/6 5/6 3/4 2/3 6/4 5/3 explain why you got that answer.

Answer 1

`(3/4)` and
`(2/3)`.

Explanation:

For a fraction of the form
`(p / q)`, the number in front of the division (
`p`) is the numerator. The number after the division (
`q`) is the denominator.

`\begin{aligned} (p)/(q) \quad \genfrac{}{}{0}{}{(\text{numerator})}{(\text{denominator})}\end{aligned}`.

A positive fraction
`(p/q)` (
`p,\, q > 0`) is less than
`1` as long as the numerator
`p` is smaller than the denominator
`q` (that is,
`p < q`.) The reason is that as long as
`p,\, q > 0`:

`\begin{aligned} & (p)/(q) < 1 \\ \iff & (q)\, \left((p)/(q)\right) < (q)\, (1) && (\text{given that $q > 0$}) \\ \iff & p < q\end{aligned}`.

For example, in the fraction
`(2/3)`,
`2` is the numerator while
`3` is the denominator. Both the numerator and the denominator are positive, while the numerator
`2\!` is smaller than the denominator
`3\!`. Therefore,
`(2/3)` would be less than
`1`.