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Answer :
To determine which ratio is equivalent to [tex]\(\frac{9}{10}\)[/tex], let's compare each given option to [tex]\(\frac{9}{10}\)[/tex] by checking if the two ratios reduce to the same simplest form. Here's how to do it:
1. Option 1: [tex]\(\frac{30}{27}\)[/tex]
- Simplify [tex]\(\frac{30}{27}\)[/tex].
- The greatest common factor (GCF) of 30 and 27 is 3.
- Dividing both numerator and denominator by 3:
[tex]\[
\frac{30 \div 3}{27 \div 3} = \frac{10}{9}
\][/tex]
- [tex]\(\frac{10}{9}\)[/tex] is not the same as [tex]\(\frac{9}{10}\)[/tex].
2. Option 2: [tex]\(\frac{27}{30}\)[/tex]
- Simplify [tex]\(\frac{27}{30}\)[/tex].
- The greatest common factor (GCF) of 27 and 30 is 3.
- Dividing both numerator and denominator by 3:
[tex]\[
\frac{27 \div 3}{30 \div 3} = \frac{9}{10}
\][/tex]
- [tex]\(\frac{9}{10}\)[/tex] is the same as [tex]\(\frac{9}{10}\)[/tex], so [tex]\(\frac{27}{30}\)[/tex] is equivalent.
3. Option 3: [tex]\(\frac{27}{20}\)[/tex]
- Simplify [tex]\(\frac{27}{20}\)[/tex].
- There is no common factor other than 1, so it is already in its simplest form.
- [tex]\(\frac{27}{20}\)[/tex] is not the same as [tex]\(\frac{9}{10}\)[/tex].
Therefore, the ratio [tex]\(\frac{27}{30}\)[/tex] is equivalent to [tex]\(\frac{9}{10}\)[/tex].
1. Option 1: [tex]\(\frac{30}{27}\)[/tex]
- Simplify [tex]\(\frac{30}{27}\)[/tex].
- The greatest common factor (GCF) of 30 and 27 is 3.
- Dividing both numerator and denominator by 3:
[tex]\[
\frac{30 \div 3}{27 \div 3} = \frac{10}{9}
\][/tex]
- [tex]\(\frac{10}{9}\)[/tex] is not the same as [tex]\(\frac{9}{10}\)[/tex].
2. Option 2: [tex]\(\frac{27}{30}\)[/tex]
- Simplify [tex]\(\frac{27}{30}\)[/tex].
- The greatest common factor (GCF) of 27 and 30 is 3.
- Dividing both numerator and denominator by 3:
[tex]\[
\frac{27 \div 3}{30 \div 3} = \frac{9}{10}
\][/tex]
- [tex]\(\frac{9}{10}\)[/tex] is the same as [tex]\(\frac{9}{10}\)[/tex], so [tex]\(\frac{27}{30}\)[/tex] is equivalent.
3. Option 3: [tex]\(\frac{27}{20}\)[/tex]
- Simplify [tex]\(\frac{27}{20}\)[/tex].
- There is no common factor other than 1, so it is already in its simplest form.
- [tex]\(\frac{27}{20}\)[/tex] is not the same as [tex]\(\frac{9}{10}\)[/tex].
Therefore, the ratio [tex]\(\frac{27}{30}\)[/tex] is equivalent to [tex]\(\frac{9}{10}\)[/tex].
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