Jai and Kim need to collect cans of food for a food drive. Jai collects [tex]\(\frac{65}{100}\)[/tex] of the total cans needed, and Kim collects [tex]\(\frac{2}{10}\)[/tex] of the total cans needed. What fraction of the total number of cans did they collect altogether?

A. [tex]\(\frac{63}{100}\)[/tex]
B. [tex]\(\frac{45}{100}\)[/tex]
C. [tex]\(\frac{67}{100}\)[/tex]
D. [tex]\(\frac{85}{100}\)[/tex]



Answer :

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]