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

Answer:

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

Step-by-step 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.

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

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 $p,\, q > 0$:

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

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 $1$.