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



Answer :

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].