We need to add the numbers 4 1/3, 2 1/3, and 6 1/2. First, let's convert them into improper fractions for easier adding:
[tex] \frac{13}{3} + \frac{7}{3} + \frac{13}{2} [/tex]
Now, since two of the fractions have the same denominator, we can simplify it, giving us this:
[tex] \frac{20}{3} + \frac{13}{2} [/tex]
Next, we have to find the least common denominator of the two fractions. The smallest number that both 2 and 3 go into is 6, so we can change our denominator to 6:
[tex]\frac{20}{3}(\frac{2}{2}) + \frac{13}{2}( \frac{3}{3})[/tex]
[tex]\frac{40}{6}+ \frac{39}{6} [/tex]
[tex]\frac{79}{6}[/tex]
For our answer, we should convert this back into a mixed number:
[tex]\frac{79}{6} = 13\frac{1}{6} [/tex]
Peter makes 13 1/6 cups of punch.
