A recipe calls for 2 1/3 cups of flour . Jane needs to make only half of the recipe. How much flour does she need?
The Correct Answer and Explanation is :
To determine how much flour Jane needs for half of a recipe that calls for (2 \frac{1}{3}) cups of flour, we first need to convert the mixed number into an improper fraction.
Step 1: Convert the Mixed Number
A mixed number consists of a whole number and a fraction. Here, (2 \frac{1}{3}) can be converted as follows:
- Multiply the whole number (2) by the denominator (3):
[
2 \times 3 = 6
] - Add the numerator (1) to this result:
[
6 + 1 = 7
] - Thus, the mixed number (2 \frac{1}{3}) can be expressed as the improper fraction (\frac{7}{3}).
Step 2: Calculate Half of the Flour
Next, we want to find half of this amount. To do this, we multiply the improper fraction (\frac{7}{3}) by (\frac{1}{2}):
[
\text{Flour needed} = \frac{7}{3} \times \frac{1}{2} = \frac{7 \times 1}{3 \times 2} = \frac{7}{6}
]
Step 3: Convert Back to Mixed Number
The improper fraction (\frac{7}{6}) can be converted back to a mixed number:
- Divide the numerator (7) by the denominator (6):
[
7 \div 6 = 1 \quad \text{(whole number)}
]
with a remainder of 1. Thus, we have (1 \frac{1}{6}).
Final Answer
Therefore, Jane needs (1 \frac{1}{6}) cups of flour to make half of the recipe.
Explanation
This process of converting mixed numbers to improper fractions and back allows for easier calculations when multiplying or dividing fractions. It simplifies the arithmetic involved, especially when scaling recipes, which is common in cooking and baking. Knowing how to work with fractions accurately is essential for precise measurement and ensuring the quality of the final dish. By carefully following these steps, anyone can adjust recipes to their needs efficiently.