Isaiah brought two dozen donuts to a class party. Half of the donuts had vanilla frosting with sprinkles, 2 had strawberry frosting with cream filling, and the rest had chocolate frosting with sprinkles. What fraction of the donuts had sprinkles? There are 12 donuts in a dozen.

Question

One-half
StartFraction 5 Over 6 EndFraction
StartFraction 7 Over 12 EndFraction

Answer 1

Isaiah brought two dozen donuts, which is \( 2 \times 12 = 24 \) donuts.

Half of the donuts had vanilla frosting with sprinkles, which is:

\[ \frac{1}{2} \times 24 = 12 \text{ donuts} \]

There are also 2 donuts with strawberry frosting with cream filling.

The remaining donuts must have chocolate frosting with sprinkles. To find the number of chocolate donuts, we subtract the number of vanilla and strawberry donuts from the total number of donuts:

\[ 24 - 12 - 2 = 10 \text{ donuts with chocolate frosting} \]

Now we can determine the total number of donuts with sprinkles. This includes the donuts with vanilla frosting (which has sprinkles) and the donuts with chocolate frosting (which also has sprinkles):

\[ 12 \text{ (vanilla)} + 10 \text{ (chocolate)} = 22 \text{ donuts with sprinkles} \]

Now we find the fraction of donuts that had sprinkles:

\[ \frac{\text{Donuts with sprinkles}}{\text{Total donuts}} = \frac{22}{24} \]

To simplify this fraction, we can divide the numerator and the denominator by 2:

\[ \frac{22 \div 2}{24 \div 2} = \frac{11}{12} \]

Thus, the fraction of the donuts that had sprinkles is:

\[ \frac{11}{12} \]

The provided answer choices do not include \( \frac{11}{12} \), so there may be a mistake in the given options. Based on the calculations made, \( \frac{11}{12} \) is the correct answer for the fraction of donuts that had sprinkles.