To determine which fractions are equivalent to [tex]\(\frac{9}{10}\)[/tex], we need to simplify each of the given fractions and compare their decimal values to the decimal value of [tex]\(\frac{9}{10}\)[/tex].
First, let's convert [tex]\(\frac{9}{10}\)[/tex] to its decimal form:
[tex]\[
\frac{9}{10} = 0.9
\][/tex]
Next, we convert each of the given fractions to their decimal forms:
1. [tex]\(\frac{5}{14}\)[/tex]:
[tex]\[
\frac{5}{14} \approx 0.357
\][/tex]
2. [tex]\(\frac{18}{20}\)[/tex]:
[tex]\[
\frac{18}{20} = 0.9
\][/tex]
3. [tex]\(\frac{27}{30}\)[/tex]:
[tex]\[
\frac{27}{30} = 0.9
\][/tex]
4. [tex]\(\frac{15}{20}\)[/tex]:
[tex]\[
\frac{15}{20} = 0.75
\][/tex]
Now, we compare each of these decimal values to the decimal value of [tex]\(\frac{9}{10}\)[/tex], which is 0.9.
- [tex]\(\frac{5}{14} \approx 0.357\)[/tex], which is not equal to 0.9.
- [tex]\(\frac{18}{20} = 0.9\)[/tex], which is equal to 0.9.
- [tex]\(\frac{27}{30} = 0.9\)[/tex], which is equal to 0.9.
- [tex]\(\frac{15}{20} = 0.75\)[/tex], which is not equal to 0.9.
Therefore, the fractions equivalent to [tex]\(\frac{9}{10}\)[/tex] are:
- [tex]\(\frac{18}{20}\)[/tex]
- [tex]\(\frac{27}{30}\)[/tex]
So the correct answers are:
B. [tex]\(\frac{18}{20}\)[/tex]
C. [tex]\(\frac{27}{30}\)[/tex]
