To find the fraction of the total number of cans that Jai and Kim collected altogether, we need to follow these steps:
1. Convert the fractions to a common denominator:
- Jai collects [tex]\(\frac{65}{100}\)[/tex] of the total cans.
- Kim collects [tex]\(\frac{2}{10}\)[/tex] of the total cans.
2. Convert Kim’s fraction to have the same denominator as Jai's fraction to make the addition easier:
- [tex]\(\frac{2}{10}\)[/tex] can be converted to a fraction with a denominator of 100:
[tex]\[
\frac{2}{10} = \frac{2 \times 10}{10 \times 10} = \frac{20}{100}
\][/tex]
3. Add the two fractions together:
- Jai’s fraction is [tex]\(\frac{65}{100}\)[/tex]
- Kim’s converted fraction is [tex]\(\frac{20}{100}\)[/tex]
- Adding these fractions:
[tex]\[
\frac{65}{100} + \frac{20}{100} = \frac{65 + 20}{100} = \frac{85}{100}
\][/tex]
Therefore, the total fraction of the cans that Jai and Kim collected together is [tex]\(\frac{85}{100}\)[/tex].
So, the correct answer is:
[tex]\[
\frac{85}{100}
\][/tex]
