Let's solve this problem step-by-step to determine what fraction of the total number of cans Jai and Kim collected altogether.
1. Determine the fraction of cans collected by Jai:
Jai collects [tex]\(\frac{65}{100}\)[/tex] of the total cans.
2. Determine the fraction of cans collected by Kim:
Kim collects [tex]\(\frac{2}{10}\)[/tex] of the total cans.
We should convert [tex]\(\frac{2}{10}\)[/tex] to have a common denominator with Jai's fraction.
[tex]\[
\frac{2}{10} = \frac{2 \times 10}{10 \times 10} = \frac{20}{100}
\][/tex]
3. Add the fractions collected by Jai and Kim:
Now, we can add the two fractions because they have the same denominator.
[tex]\[
\frac{65}{100} + \frac{20}{100} = \frac{65 + 20}{100} = \frac{85}{100}
\][/tex]
4. Simplify the fraction, if possible:
The fraction [tex]\(\frac{85}{100}\)[/tex] is already in its simplest form.
Thus, the fraction of the total number of cans that Jai and Kim collected altogether is [tex]\(\frac{85}{100}\)[/tex].
Therefore, the correct answer is [tex]\(\boxed{\frac{85}{100}}\)[/tex].
