To express 9.5 as a fraction in its simplest form, let's analyze the given options:
1. [tex]\(\frac{86}{9}\)[/tex]
2. [tex]\(\frac{19}{2}\)[/tex]
3. [tex]\(\frac{46}{5}\)[/tex]
4. [tex]\(\frac{64}{7}\)[/tex]
First, we need to express 9.5 as a fraction. The decimal 9.5 can be written as:
[tex]\[ 9.5 = \frac{95}{10} \][/tex]
To simplify [tex]\(\frac{95}{10}\)[/tex], we divide both the numerator and the denominator by their greatest common divisor (GCD), which in this case is 5:
[tex]\[ \frac{95 \div 5}{10 \div 5} = \frac{19}{2} \][/tex]
Thus, 9.5 expressed as a fraction in simplest form is:
[tex]\[ \frac{19}{2} \][/tex]
Now, let's match this fraction with the given options:
- [tex]\(\frac{86}{9}\)[/tex] is not equal to [tex]\(\frac{19}{2}\)[/tex]
- [tex]\(\frac{19}{2}\)[/tex] is exactly what we have found to be the simplest form of 9.5
- [tex]\(\frac{46}{5}\)[/tex] is not equal to [tex]\(\frac{19}{2}\)[/tex]
- [tex]\(\frac{64}{7}\)[/tex] is not equal to [tex]\(\frac{19}{2}\)[/tex]
Therefore, the correct choice is:
[tex]\(\boxed{\frac{19}{2}}\)[/tex]
