Peter mixes $4 \frac{1}{3}$ cups of orange juice, $2 \frac{1}{3}$ cups of ginger ale, and $6 \frac{1}{2}$ cups of strawberry lemonade to make some punch. What is the total number of cups of punch that Peter makes?
A. $13 \frac{1}{6}$
B. $12 \frac{3}{8}$
C. $12 \frac{3}{5}$
D. $12 \frac{1}{2}$
Answer (1)
Convert all mixed numbers to improper fractions: 4 3 1 = 3 13 , 2 3 1 = 3 7 , 6 2 1 = 2 13 .
Find a common denominator (6) and convert the fractions: 6 26 + 6 14 + 6 39 .
Add the fractions: 6 26 + 14 + 39 = 6 79 .
Convert the improper fraction back to a mixed number: 6 79 = 13 6 1 . The total number of cups of punch is 13 6 1 .
Explanation
Understanding the Problem We are given the amounts of three ingredients in cups: orange juice ( 4 3 1 ), ginger ale ( 2 3 1 ), and strawberry lemonade ( 6 2 1 ). We need to find the total amount of punch by adding these three quantities.
Converting to Improper Fractions First, let's convert each mixed number to an improper fraction.
For orange juice: 4 3 1 = 3 4 × 3 + 1 = 3 12 + 1 = 3 13 cups.
For ginger ale: 2 3 1 = 3 2 × 3 + 1 = 3 6 + 1 = 3 7 cups.
For strawberry lemonade: 6 2 1 = 2 6 × 2 + 1 = 2 12 + 1 = 2 13 cups.
Adding the Fractions Now, we add the three fractions: 3 13 + 3 7 + 2 13 To add these fractions, we need a common denominator. The least common multiple of 3 and 2 is 6. So we convert each fraction to have a denominator of 6:
3 13 = 3 × 2 13 × 2 = 6 26 3 7 = 3 × 2 7 × 2 = 6 14 2 13 = 2 × 3 13 × 3 = 6 39 Now we can add them: 6 26 + 6 14 + 6 39 = 6 26 + 14 + 39 = 6 79
Converting Back to Mixed Number and Final Answer Finally, we convert the improper fraction 6 79 back to a mixed number. We divide 79 by 6:
79 ÷ 6 = 13 with a remainder of 1. So, 6 79 = 13 6 1 .
Therefore, the total number of cups of punch is 13 6 1 cups.
Examples
Mixing ingredients to create a recipe is a common application of adding fractions. For instance, if you're baking a cake and need 2 2 1 cups of flour, 1 4 1 cups of sugar, and 4 3 cup of butter, you would add these amounts to determine the total volume of dry ingredients. This ensures you have the correct proportions for your recipe, leading to a delicious outcome. Understanding how to add mixed numbers and fractions is essential for accurate measurements and successful cooking or baking.
