The liquid portion of a recipe calls for 1/4 cup of soy sauce, 1 1/2 cups of pineapple juice, and 2 2/3 cups of chicken broth. Altogether, how many cups of liquid are used in the recipe?
Answer (1)
Convert mixed numbers to improper fractions.
Find a common denominator for the fractions.
Add the fractions.
Convert the resulting improper fraction back to a mixed number: 4 12 5 cups.
Explanation
Problem Analysis We need to find the total amount of liquid in the recipe. The recipe calls for 4 1 cup of soy sauce, 1 2 1 cups of pineapple juice, and 2 3 2 cups of chicken broth. To find the total, we need to add these three amounts together.
Converting Mixed Numbers to Improper Fractions First, let's convert the mixed numbers to improper fractions. We have:
1 2 1 = 2 1 × 2 + 1 = 2 3
2 3 2 = 3 2 × 3 + 2 = 3 8
Adding the Fractions Now, we add the three fractions:
4 1 + 2 3 + 3 8
Finding a Common Denominator To add these fractions, we need to find a common denominator. The least common multiple of 4, 2, and 3 is 12. So, we convert each fraction to have a denominator of 12:
4 1 = 4 × 3 1 × 3 = 12 3
2 3 = 2 × 6 3 × 6 = 12 18
3 8 = 3 × 4 8 × 4 = 12 32
Adding the Fractions with Common Denominator Now we can add the fractions:
12 3 + 12 18 + 12 32 = 12 3 + 18 + 32 = 12 53
Converting Back to Mixed Number Finally, we convert the improper fraction 12 53 back to a mixed number:
12 53 = 4 12 5
Final Answer Therefore, the total amount of liquid used in the recipe is 4 12 5 cups.
Examples
In baking, accurately measuring liquid ingredients is crucial for the recipe's success. For instance, if you're making a cake and need a specific amount of liquid from multiple sources like milk, juice, and melted butter, you must add these volumes together correctly. This problem demonstrates how to combine fractional and mixed number quantities, ensuring the right consistency and flavor in your baked goods. Understanding these calculations prevents errors and helps achieve the desired outcome in your culinary creations.
