Answer :
To determine which of the given fractions is equivalent to [tex]\(\frac{9}{10}\)[/tex], let's analyze each option provided.
### Option A: [tex]\(\frac{27}{40}\)[/tex]
First, convert [tex]\(\frac{27}{40}\)[/tex] to a decimal to compare it with [tex]\(\frac{9}{10}\)[/tex]:
[tex]\[
\frac{27}{40} = 0.675
\][/tex]
The fraction [tex]\( \frac{9}{10} \)[/tex] as a decimal is:
[tex]\[
\frac{9}{10} = 0.9
\][/tex]
Comparing [tex]\(0.675\)[/tex] and [tex]\(0.9\)[/tex], we see they are not equal. Therefore, [tex]\(\frac{27}{40}\)[/tex] is not equivalent to [tex]\(\frac{9}{10}\)[/tex].
### Option B: [tex]\(\frac{18}{30}\)[/tex]
Next, convert [tex]\(\frac{18}{30}\)[/tex] to a decimal:
[tex]\[
\frac{18}{30} = 0.6
\][/tex]
Again, compare it to the decimal value of [tex]\(\frac{9}{10}\)[/tex]:
[tex]\[
\frac{9}{10} = 0.9
\][/tex]
Here, [tex]\(0.6\)[/tex] and [tex]\(0.9\)[/tex] are not equal. Thus, [tex]\(\frac{18}{30}\)[/tex] is also not equivalent to [tex]\(\frac{9}{10}\)[/tex].
### Option C: [tex]\(\frac{36}{40}\)[/tex]
Finally, convert [tex]\(\frac{36}{40}\)[/tex] to a decimal:
[tex]\[
\frac{36}{40} = 0.9
\][/tex]
Compare it to the decimal value of [tex]\(\frac{9}{10}\)[/tex]:
[tex]\[
\frac{9}{10} = 0.9
\][/tex]
Since both are equal, [tex]\(\frac{36}{40}\)[/tex] is equivalent to [tex]\(\frac{9}{10}\)[/tex].
### Conclusion
After comparing all options, the fraction that is equivalent to [tex]\(\frac{9}{10}\)[/tex] is:
[tex]\[
\boxed{\frac{36}{40}}
\][/tex]
### Option A: [tex]\(\frac{27}{40}\)[/tex]
First, convert [tex]\(\frac{27}{40}\)[/tex] to a decimal to compare it with [tex]\(\frac{9}{10}\)[/tex]:
[tex]\[
\frac{27}{40} = 0.675
\][/tex]
The fraction [tex]\( \frac{9}{10} \)[/tex] as a decimal is:
[tex]\[
\frac{9}{10} = 0.9
\][/tex]
Comparing [tex]\(0.675\)[/tex] and [tex]\(0.9\)[/tex], we see they are not equal. Therefore, [tex]\(\frac{27}{40}\)[/tex] is not equivalent to [tex]\(\frac{9}{10}\)[/tex].
### Option B: [tex]\(\frac{18}{30}\)[/tex]
Next, convert [tex]\(\frac{18}{30}\)[/tex] to a decimal:
[tex]\[
\frac{18}{30} = 0.6
\][/tex]
Again, compare it to the decimal value of [tex]\(\frac{9}{10}\)[/tex]:
[tex]\[
\frac{9}{10} = 0.9
\][/tex]
Here, [tex]\(0.6\)[/tex] and [tex]\(0.9\)[/tex] are not equal. Thus, [tex]\(\frac{18}{30}\)[/tex] is also not equivalent to [tex]\(\frac{9}{10}\)[/tex].
### Option C: [tex]\(\frac{36}{40}\)[/tex]
Finally, convert [tex]\(\frac{36}{40}\)[/tex] to a decimal:
[tex]\[
\frac{36}{40} = 0.9
\][/tex]
Compare it to the decimal value of [tex]\(\frac{9}{10}\)[/tex]:
[tex]\[
\frac{9}{10} = 0.9
\][/tex]
Since both are equal, [tex]\(\frac{36}{40}\)[/tex] is equivalent to [tex]\(\frac{9}{10}\)[/tex].
### Conclusion
After comparing all options, the fraction that is equivalent to [tex]\(\frac{9}{10}\)[/tex] is:
[tex]\[
\boxed{\frac{36}{40}}
\][/tex]
