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?

Question

the answer is fraction!

Answer 1

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: $$\frac{3}{8}$$