Question

antonio has \\(\frac{1}{2}\\) cup of flour at his house. one cake needs \\(2\frac{1}{4}\\) cups of flour. so how much of a cake can antonio make?

Explanation:

Step1: Convert mixed number to improper fraction

The amount of flour needed for one cake is \(2\frac{1}{4}\) cups. To convert this mixed number to an improper fraction, we use the formula \(a\frac{b}{c}=\frac{a\times c + b}{c}\). So, \(2\frac{1}{4}=\frac{2\times4 + 1}{4}=\frac{9}{4}\) cups.

Step2: Divide the available flour by flour needed per cake

Antonio has \(\frac{1}{2}\) cup of flour. To find out how much of a cake he can make, we divide the available flour by the flour needed per cake. That is \(\frac{1}{2}\div\frac{9}{4}\). When dividing fractions, we multiply by the reciprocal, so \(\frac{1}{2}\times\frac{4}{9}=\frac{4}{18}=\frac{2}{9}\).

Answer:

\(\frac{2}{9}\) of a cake