Answer:
The answers are [tex]\frac{2}{5}, \frac{1}{4}, \frac{1}{10}, \frac{5}{2}, \frac{5}{8}, \frac{4}{1}, \frac{8}{5},[/tex] and [tex]\frac{10}{1}[/tex].
Step-by-step explanation:
Proportions are fractions that can be made by using the given numbers, which in this case are 2, 5, 8, and 20. Let's pair each one with the other three and then simplify if possible.
First, let's begin with 2:
[tex]\frac{2}{5} = \frac{2}{5}[/tex]
[tex]\frac{2}{8} = \frac{1}{4}[/tex]
[tex]\frac{2}{20} = \frac{1}{10}[/tex]
Then, let's do 5:
[tex]\frac{5}{2} = \frac{5}{2}[/tex]
[tex]\frac{5}{8} = \frac{5}{8}[/tex]
[tex]\frac{5}{20} = \frac{1}{4}[/tex]
Note that we already have [tex]\frac{1}{4}[/tex], so we do not need to include an additional one.
Now, let us do 8:
[tex]\frac{8}{2} = \frac{4}{1}[/tex]
[tex]\frac{8}{5} = \frac{8}{5}[/tex]
[tex]\frac{8}{20} = \frac{2}{5}[/tex]
See how we already have [tex]\frac{2}{5}[/tex], so we won't have to include that as well.
Finally, let's do 20:
[tex]\frac{20}{2} = \frac{10}{1}[/tex]
[tex]\frac{20}{5} = \frac{4}{1}[/tex]
[tex]\frac{20}{8} = \frac{5}{2}[/tex]
Now see that we already have both [tex]\frac{4}{1}[/tex] and [tex]\frac{5}{2}[/tex], so we won't have to include both of them, as they are both extras.
Hence, the answers are [tex]\frac{2}{5}, \frac{1}{4}, \frac{1}{10}, \frac{5}{2}, \frac{5}{8}, \frac{4}{1}, \frac{8}{5},[/tex] and [tex]\frac{10}{1}[/tex].
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