Question

annie is making cakes for a bake sale. she needs 1\frac{1}{3} cups of sugar for a chocolate cake and 2\frac{3}{5} cups of sugar for a strawberry cake. how much more sugar does she need to make the chocolate cake?\
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a. 4\
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b. 1\frac{4}{15}\
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c. 3\frac{6}{15}\
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d. 4\frac{2}{15}

Explanation:

Step1: Identify the operation

To find how much more sugar is needed for the strawberry cake (wait, the question says "how much more sugar does she need to make the chocolate cake?" Wait, no—wait, the strawberry cake needs \(2\frac{3}{5}\) cups, chocolate needs \(1\frac{1}{3}\) cups. Wait, maybe the question has a typo? Wait, no—wait, "how much more sugar does she need to make the chocolate cake?" No, that doesn't make sense. Wait, maybe it's "how much more sugar does she need for the strawberry cake than the chocolate cake?" Because \(2\frac{3}{5}\) is more than \(1\frac{1}{3}\). Let's assume that: find the difference between \(2\frac{3}{5}\) and \(1\frac{1}{3}\).

Step2: Convert mixed numbers to improper fractions

\(2\frac{3}{5}=\frac{2\times5 + 3}{5}=\frac{13}{5}\)

\(1\frac{1}{3}=\frac{1\times3 + 1}{3}=\frac{4}{3}\)

Step3: Find a common denominator

The denominators are 5 and 3, so the least common denominator is 15.

Convert \(\frac{13}{5}\) to fifteenths: \(\frac{13}{5}=\frac{13\times3}{5\times3}=\frac{39}{15}\)

Convert \(\frac{4}{3}\) to fifteenths: \(\frac{4}{3}=\frac{4\times5}{3\times5}=\frac{20}{15}\)

Step4: Subtract the fractions

\(\frac{39}{15}-\frac{20}{15}=\frac{39 - 20}{15}=\frac{19}{15}\)

Step5: Convert back to mixed number

\(\frac{19}{15}=1\frac{4}{15}\)

Wait, but the options include B: \(1\frac{4}{15}\). Wait, but let's check the question again: "how much more sugar does she need to make the chocolate cake?" That seems reversed. Wait, maybe the question is "how much more sugar does she need for the strawberry cake than the chocolate cake?" Because \(2\frac{3}{5}\) is more than \(1\frac{1}{3}\). So the difference is \(2\frac{3}{5}-1\frac{1}{3}=1\frac{4}{15}\), which is option B.

Answer:

B. \(1\frac{4}{15}\)