A jar holds 3 1/2 cups of water. How much is this in fluid ounces?
The Correct Answer and Explanation is:
To convert cups to fluid ounces, it is important to understand the relationship between these two units of measurement. One cup is equivalent to 8 fluid ounces. Therefore, to convert 3 1/2 cups of water to fluid ounces, we can follow these steps:
- Convert the mixed number to an improper fraction:
(3 \frac{1}{2}) cups can be converted to an improper fraction by multiplying the whole number (3) by the denominator (2) and then adding the numerator (1).
[
3 \times 2 + 1 = 6 + 1 = 7
]
So, (3 \frac{1}{2} = \frac{7}{2}) cups. - Multiply the number of cups by the conversion factor (8 fluid ounces per cup):
Now that we have ( \frac{7}{2} ) cups, we can multiply this by 8 fluid ounces per cup to convert to fluid ounces:
[
\frac{7}{2} \times 8 = \frac{7 \times 8}{2} = \frac{56}{2} = 28
]
Therefore, (3 \frac{1}{2}) cups of water is equivalent to 28 fluid ounces.
Explanation of the Conversion Process
The conversion of cups to fluid ounces is essential in various contexts, especially in cooking, baking, and liquid measurements. Understanding this conversion can help ensure that recipes are followed accurately, as incorrect measurements can lead to undesirable results in food preparation.
In the United States, the cup is a common unit for measuring volume in cooking. Many recipes specify ingredients in cups, but it may also be necessary to convert these measurements to fluid ounces, especially when working with pre-packaged ingredients or when using measuring tools that mark fluid ounces.
The method described above provides a systematic way to convert between these two units. First, by converting mixed numbers to improper fractions, we simplify calculations. Then, multiplying by the conversion factor allows us to obtain the desired measurement in fluid ounces. This mathematical process is foundational for anyone working in culinary arts or science where precision in measurements is crucial. Understanding unit conversions can also improve numerical literacy, enabling better decision-making in daily tasks.