Question
At the donut shop, 1/2 of their donuts have frosting. Of the donuts with frosting, 3/4 of them have sprinkles. How many donuts have both frosting and sprinkles?
the answer is fraction!
the answer is fraction!
Answers
GPT-4o mini
To determine the fraction of donuts that have both frosting and sprinkles, we can start from the beginning.
Let’s assume the total number of donuts at the shop is \( D \).
1. **Donuts with Frosting**:
According to the problem, \( \frac{1}{2} \) of the donuts have frosting. So, the number of donuts with frosting is:
\[
\frac{1}{2} D
\]
2. **Donuts with Sprinkles**:
Of the donuts that have frosting, \( \frac{3}{4} \) have sprinkles. Therefore, the number of donuts that have both frosting and sprinkles is:
\[
\frac{3}{4} \times \text{(donuts with frosting)} = \frac{3}{4} \times \frac{1}{2} D
\]
3. **Calculating the Fraction**:
Now calculate \( \frac{3}{4} \times \frac{1}{2} D \):
\[
\frac{3}{4} \times \frac{1}{2} D = \frac{3 \times 1}{4 \times 2} D = \frac{3}{8} D
\]
Thus, the fraction of the total donuts that have both frosting and sprinkles is \( \frac{3}{8} \).
Therefore, the final answer is:
\[
\frac{3}{8}
\]
Let’s assume the total number of donuts at the shop is \( D \).
1. **Donuts with Frosting**:
According to the problem, \( \frac{1}{2} \) of the donuts have frosting. So, the number of donuts with frosting is:
\[
\frac{1}{2} D
\]
2. **Donuts with Sprinkles**:
Of the donuts that have frosting, \( \frac{3}{4} \) have sprinkles. Therefore, the number of donuts that have both frosting and sprinkles is:
\[
\frac{3}{4} \times \text{(donuts with frosting)} = \frac{3}{4} \times \frac{1}{2} D
\]
3. **Calculating the Fraction**:
Now calculate \( \frac{3}{4} \times \frac{1}{2} D \):
\[
\frac{3}{4} \times \frac{1}{2} D = \frac{3 \times 1}{4 \times 2} D = \frac{3}{8} D
\]
Thus, the fraction of the total donuts that have both frosting and sprinkles is \( \frac{3}{8} \).
Therefore, the final answer is:
\[
\frac{3}{8}
\]
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