Answer :
Sure! To determine which of the given ratios are equivalent to [tex]\(\frac{9}{18}\)[/tex], we need to simplify or compare each option. Here’s how you can do it step-by-step:
1. Simplify the original fraction:
- [tex]\(\frac{9}{18}\)[/tex] can be simplified by dividing both the numerator (top) and the denominator (bottom) by their greatest common divisor, which is 9.
- [tex]\(\frac{9 ÷ 9}{18 ÷ 9} = \frac{1}{2}\)[/tex]
So, we are looking for ratios or fractions that equal [tex]\(\frac{1}{2}\)[/tex].
2. Check each given option:
- Option A: [tex]\(25:50\)[/tex]
- This can be written as the fraction [tex]\(\frac{25}{50}\)[/tex].
- Simplify by dividing both the numerator and the denominator by 25.
- [tex]\(\frac{25 ÷ 25}{50 ÷ 25} = \frac{1}{2}\)[/tex]
- This is equivalent to [tex]\(\frac{1}{2}\)[/tex].
- Option B: [tex]\(\frac{2}{1}\)[/tex]
- This fraction is already simplified and is [tex]\(\frac{2}{1}\)[/tex].
- [tex]\(\frac{2}{1}\)[/tex] is not equivalent to [tex]\(\frac{1}{2}\)[/tex].
- Option C: 75 to 150
- This can be written as the fraction [tex]\(\frac{75}{150}\)[/tex].
- Simplify by dividing both the numerator and the denominator by 75.
- [tex]\(\frac{75 ÷ 75}{150 ÷ 75} = \frac{1}{2}\)[/tex]
- This is equivalent to [tex]\(\frac{1}{2}\)[/tex].
- Option D: [tex]\(125:250\)[/tex]
- This can be written as the fraction [tex]\(\frac{125}{250}\)[/tex].
- Simplify by dividing both the numerator and the denominator by 125.
- [tex]\(\frac{125 ÷ 125}{250 ÷ 125} = \frac{1}{2}\)[/tex]
- This is equivalent to [tex]\(\frac{1}{2}\)[/tex].
- Option E: 18 to 38
- This can be written as the fraction [tex]\(\frac{18}{38}\)[/tex].
- Simplify by dividing both the numerator and the denominator by their greatest common divisor, which in this case is 2.
- [tex]\(\frac{18 ÷ 2}{38 ÷ 2} = \frac{9}{19}\)[/tex]
- [tex]\(\frac{9}{19}\)[/tex] is not equivalent to [tex]\(\frac{1}{2}\)[/tex].
- Option F: [tex]\(\frac{54}{27}\)[/tex]
- Simplify by dividing both the numerator and the denominator by their greatest common divisor, which is 27.
- [tex]\(\frac{54 ÷ 27}{27 ÷ 27} = \frac{2}{1}\)[/tex]
- [tex]\(\frac{2}{1}\)[/tex] is not equivalent to [tex]\(\frac{1}{2}\)[/tex].
3. Conclusion:
The ratios or fractions that are equivalent to [tex]\(\frac{9}{18}\)[/tex] or [tex]\(\frac{1}{2}\)[/tex] are:
- [tex]\( 25:50 \)[/tex] (Option A)
- [tex]\( 75:150 \)[/tex] (Option C)
- [tex]\( 125:250 \)[/tex] (Option D)
So, the correct answer is A, C, and D.
1. Simplify the original fraction:
- [tex]\(\frac{9}{18}\)[/tex] can be simplified by dividing both the numerator (top) and the denominator (bottom) by their greatest common divisor, which is 9.
- [tex]\(\frac{9 ÷ 9}{18 ÷ 9} = \frac{1}{2}\)[/tex]
So, we are looking for ratios or fractions that equal [tex]\(\frac{1}{2}\)[/tex].
2. Check each given option:
- Option A: [tex]\(25:50\)[/tex]
- This can be written as the fraction [tex]\(\frac{25}{50}\)[/tex].
- Simplify by dividing both the numerator and the denominator by 25.
- [tex]\(\frac{25 ÷ 25}{50 ÷ 25} = \frac{1}{2}\)[/tex]
- This is equivalent to [tex]\(\frac{1}{2}\)[/tex].
- Option B: [tex]\(\frac{2}{1}\)[/tex]
- This fraction is already simplified and is [tex]\(\frac{2}{1}\)[/tex].
- [tex]\(\frac{2}{1}\)[/tex] is not equivalent to [tex]\(\frac{1}{2}\)[/tex].
- Option C: 75 to 150
- This can be written as the fraction [tex]\(\frac{75}{150}\)[/tex].
- Simplify by dividing both the numerator and the denominator by 75.
- [tex]\(\frac{75 ÷ 75}{150 ÷ 75} = \frac{1}{2}\)[/tex]
- This is equivalent to [tex]\(\frac{1}{2}\)[/tex].
- Option D: [tex]\(125:250\)[/tex]
- This can be written as the fraction [tex]\(\frac{125}{250}\)[/tex].
- Simplify by dividing both the numerator and the denominator by 125.
- [tex]\(\frac{125 ÷ 125}{250 ÷ 125} = \frac{1}{2}\)[/tex]
- This is equivalent to [tex]\(\frac{1}{2}\)[/tex].
- Option E: 18 to 38
- This can be written as the fraction [tex]\(\frac{18}{38}\)[/tex].
- Simplify by dividing both the numerator and the denominator by their greatest common divisor, which in this case is 2.
- [tex]\(\frac{18 ÷ 2}{38 ÷ 2} = \frac{9}{19}\)[/tex]
- [tex]\(\frac{9}{19}\)[/tex] is not equivalent to [tex]\(\frac{1}{2}\)[/tex].
- Option F: [tex]\(\frac{54}{27}\)[/tex]
- Simplify by dividing both the numerator and the denominator by their greatest common divisor, which is 27.
- [tex]\(\frac{54 ÷ 27}{27 ÷ 27} = \frac{2}{1}\)[/tex]
- [tex]\(\frac{2}{1}\)[/tex] is not equivalent to [tex]\(\frac{1}{2}\)[/tex].
3. Conclusion:
The ratios or fractions that are equivalent to [tex]\(\frac{9}{18}\)[/tex] or [tex]\(\frac{1}{2}\)[/tex] are:
- [tex]\( 25:50 \)[/tex] (Option A)
- [tex]\( 75:150 \)[/tex] (Option C)
- [tex]\( 125:250 \)[/tex] (Option D)
So, the correct answer is A, C, and D.
