Answer :
To determine which ratio is equivalent to [tex]\(71:17\)[/tex], we need to compare each provided option to the original ratio of [tex]\(71:17\)[/tex].
1. Original Ratio: This is [tex]\(71:17\)[/tex].
2. Option 1: [tex]\(\frac{17}{1}\)[/tex]
This is the same as saying [tex]\(17:1\)[/tex]. To check if it's equivalent, we'd compare [tex]\(\frac{17}{1}\)[/tex] to [tex]\(\frac{71}{17}\)[/tex]. These are not equivalent because [tex]\(\frac{17}{1} = 17\)[/tex] and [tex]\(\frac{71}{17} \neq 17\)[/tex].
3. Option 2: [tex]\(\frac{1}{17}\)[/tex]
This would mean [tex]\(1:17\)[/tex]. Check [tex]\(\frac{1}{17}\)[/tex] against [tex]\(\frac{71}{17}\)[/tex]. These are clearly not equivalent because [tex]\(\frac{1}{17}\)[/tex] is much smaller than [tex]\(\frac{71}{17}\)[/tex].
4. Option 3: [tex]\(71\)[/tex] to [tex]\(17\)[/tex]
This is exactly the original ratio. So, it is equivalent by definition.
5. Option 4: [tex]\(17:71\)[/tex]
This would be [tex]\(\frac{17}{71}\)[/tex]. When compared to [tex]\(\frac{71}{17}\)[/tex], these are not equivalent as [tex]\(\frac{17}{71}\)[/tex] is not equal to [tex]\(\frac{71}{17}\)[/tex].
The equivalent ratio is therefore [tex]\(71\)[/tex] to [tex]\(17\)[/tex]. This matches the original ratio exactly.
1. Original Ratio: This is [tex]\(71:17\)[/tex].
2. Option 1: [tex]\(\frac{17}{1}\)[/tex]
This is the same as saying [tex]\(17:1\)[/tex]. To check if it's equivalent, we'd compare [tex]\(\frac{17}{1}\)[/tex] to [tex]\(\frac{71}{17}\)[/tex]. These are not equivalent because [tex]\(\frac{17}{1} = 17\)[/tex] and [tex]\(\frac{71}{17} \neq 17\)[/tex].
3. Option 2: [tex]\(\frac{1}{17}\)[/tex]
This would mean [tex]\(1:17\)[/tex]. Check [tex]\(\frac{1}{17}\)[/tex] against [tex]\(\frac{71}{17}\)[/tex]. These are clearly not equivalent because [tex]\(\frac{1}{17}\)[/tex] is much smaller than [tex]\(\frac{71}{17}\)[/tex].
4. Option 3: [tex]\(71\)[/tex] to [tex]\(17\)[/tex]
This is exactly the original ratio. So, it is equivalent by definition.
5. Option 4: [tex]\(17:71\)[/tex]
This would be [tex]\(\frac{17}{71}\)[/tex]. When compared to [tex]\(\frac{71}{17}\)[/tex], these are not equivalent as [tex]\(\frac{17}{71}\)[/tex] is not equal to [tex]\(\frac{71}{17}\)[/tex].
The equivalent ratio is therefore [tex]\(71\)[/tex] to [tex]\(17\)[/tex]. This matches the original ratio exactly.
