A recipe calls for 3 3/4 cups of milk.If the measuring cup holds only 1/4 cup , how many times will you have to fill it ?
The Correct Answer and Explanation is :
To determine how many times you need to fill a 1/4 cup measuring cup to get a total of 3 3/4 cups of milk, we can follow these steps:
- Convert the Mixed Number to an Improper Fraction:
- The mixed number (3 \frac{3}{4}) can be converted to an improper fraction. To do this, multiply the whole number (3) by the denominator (4) and then add the numerator (3):
[
3 \times 4 + 3 = 12 + 3 = 15
] - Thus, (3 \frac{3}{4} = \frac{15}{4}).
- Set Up the Division:
- We need to divide the total amount of milk (in improper fraction form) by the capacity of the measuring cup:
[
\frac{15}{4} \div \frac{1}{4}
]
- Perform the Division:
- Dividing fractions involves multiplying by the reciprocal of the divisor. Thus:
[
\frac{15}{4} \div \frac{1}{4} = \frac{15}{4} \times \frac{4}{1} = \frac{15 \times 4}{4 \times 1} = \frac{15}{1} = 15
]
This calculation shows that you will need to fill the 1/4 cup measuring cup 15 times to get a total of 3 3/4 cups of milk.
Explanation
The concept of measuring ingredients accurately is essential in cooking and baking. Recipes specify ingredient quantities to ensure the dish turns out as intended. In this case, knowing how to convert mixed numbers to improper fractions allows for straightforward calculations. This method is especially useful when dealing with different measuring cup sizes.
When dividing fractions, the process becomes efficient by flipping the second fraction and multiplying. This technique simplifies the operation and helps avoid mistakes. Ensuring you have the right number of servings or the correct flavor balance depends heavily on accurate measurements.
Using a smaller measuring cup can sometimes make it easier to handle large quantities, allowing for better control over pouring and reducing spills. It’s important to have a clear understanding of how many fills are required, especially in larger recipes, to maintain the intended taste and texture of the final dish.