To find the total number of cups of punch that Peter makes, we need to add the amounts of orange juice, ginger ale, and strawberry lemonade together.
First, we convert each mixed number to an improper fraction:
-
Orange juice: \[ 4 \frac{1}{4} = 4 + \frac{1}{4} = \frac{16}{4} + \frac{1}{4} = \frac{17}{4} \]
-
Ginger ale: \[ 2 \frac{1}{4} = 2 + \frac{1}{4} = \frac{8}{4} + \frac{1}{4} = \frac{9}{4} \]
-
Strawberry lemonade: \[ 6 \frac{1}{3} = 6 + \frac{1}{3} = \frac{18}{3} + \frac{1}{3} = \frac{19}{3} \]
Now, we need to find the total by adding these improper fractions: \[ \frac{17}{4} + \frac{9}{4} + \frac{19}{3} \]
First, we can add the fractions with a common denominator. The common denominator for \(\frac{17}{4}\) and \(\frac{9}{4}\) is 4. So we add these two: \[ \frac{17}{4} + \frac{9}{4} = \frac{17 + 9}{4} = \frac{26}{4} = \frac{13}{2} \]
Now we have to add \(\frac{13}{2}\) and \(\frac{19}{3}\). The least common denominator for 2 and 3 is 6. Now we convert both fractions to have a denominator of 6: \[ \frac{13}{2} = \frac{13 \times 3}{2 \times 3} = \frac{39}{6} \] \[ \frac{19}{3} = \frac{19 \times 2}{3 \times 2} = \frac{38}{6} \]
Now we can add these two fractions: \[ \frac{39}{6} + \frac{38}{6} = \frac{39 + 38}{6} = \frac{77}{6} \]
Now we can convert the improper fraction \(\frac{77}{6}\) back into a mixed number: \[ \frac{77}{6} = 12 \frac{5}{6} \]
So the total number of cups of punch that Peter makes is: \[ \boxed{12 \frac{5}{6}} \]
1 answer