Pregunta
You need \( 1 \frac{1}{4} \) cups of sugar to make 20 cookies To make 12 cookies, you will need \( \square \) cups of sugar. Enter your answer as a fraction or whole number.
Ask by Hobbs Knight. in the United States
Jan 27,2025
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To make 12 cookies, you will need \( \frac{3}{4} \) cups of sugar.
Solución
To determine how many cups of sugar are needed to make 12 cookies, we can set up a proportion based on the given information.
1. **Understand the given information:**
- **Amount of sugar for 20 cookies:** \( 1 \frac{1}{4} \) cups.
2. **Convert the mixed number to an improper fraction:**
\[
1 \frac{1}{4} = \frac{5}{4} \text{ cups}
\]
3. **Determine the amount of sugar needed per cookie:**
\[
\text{Sugar per cookie} = \frac{\frac{5}{4} \text{ cups}}{20 \text{ cookies}} = \frac{5}{4} \times \frac{1}{20} = \frac{5}{80} = \frac{1}{16} \text{ cups per cookie}
\]
4. **Calculate the total sugar needed for 12 cookies:**
\[
\text{Total sugar} = 12 \text{ cookies} \times \frac{1}{16} \text{ cups per cookie} = \frac{12}{16} = \frac{3}{4} \text{ cups}
\]
**Answer:** \( \frac{3}{4} \) cups of sugar are needed to make 12 cookies.
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Bonus Knowledge
To determine how much sugar you need for 12 cookies, first calculate the sugar needed per cookie. You use \( 1 \frac{1}{4} \) cups of sugar for 20 cookies, which converts to \( \frac{5}{4} \) cups. So, for 1 cookie, you need \( \frac{5}{4} \div 20 = \frac{5}{80} = \frac{1}{16} \) cups of sugar. For 12 cookies, multiply \( \frac{1}{16} \) by 12: \( \frac{1}{16} \times 12 = \frac{12}{16} = \frac{3}{4} \) cups. Thus, you will need \( \frac{3}{4} \) cups of sugar to make 12 cookies.
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