Question

Order the numbers from least to greatest3 and 39/40,3 and 19/20,3 and 1/2.

Answer 1

`3(1)/(2),\text{ 3}(19)/(20)\text{ and 3}(39)/(40)`

Expanation:
`3(39)/(40),\text{ 3}(19)/(20),\text{ 3}(1)/(2)`

We need to find the LCM to determine the smallest to the greatest:

`\begin{gathered} \text{All thr}e\text{ numbers have whole numbers as 3} \\ So\text{ we will find the LCM of the fraction:} \\ (39)/(40),\text{ }(19)/(20),\text{ }(1)/(2) \\ =\frac{1(39),\text{ 2(19), 20(1)}}{40} \end{gathered}`
`\begin{gathered} =\frac{39,\text{ 38, 20}}{40} \\ \text{The numbers: }(39)/(40),\text{ }(38)/(40),(20)/(40) \\ \text{SInce they have same base, we consider the numerator:} \\ \text{The highest is 39, followed by 38 and the least is 20} \end{gathered}`
`\begin{gathered} \text{least: 20/40 represents 1/2} \\ \frac{38}{40\text{ }}represents\text{ 19/20} \\ \text{highest: 39/40 represents 39/40} \end{gathered}`
`\begin{gathered} \text{Arrangement from least to greatest:} \\ 3(1)/(2),\text{ 3}(19)/(20)\text{ and 3}(39)/(40) \end{gathered}`