- Convert the mixed fractions to improper fractions: \(3 \frac{1}{4} = \frac{13}{4}\) and \(2 \frac{2}{3} = \frac{8}{3}\).
- Find a common denominator of 12 for the fractions \(\frac{13}{4}\) and \(\frac{8}{3}\).
- Express the fractions with the common denominator: \(\frac{39}{12}\) and \(\frac{32}{12}\).
- Subtract the quantities to get the difference: \(\frac{39}{12} - \frac{32}{12} = \boxed{\frac{7}{12}}\).
Explanation
- Data and Problem Analysis
We are given that Cho uses \(2 \frac{2}{3}\) cups of flour for a cake and \(3 \frac{1}{4}\) cups of flour for a loaf of bread. To determine how much more flour she uses for the bread than the cake, we need to calculate the difference: \((3 \frac{1}{4}) - (2 \frac{2}{3})\).
- Converting Mixed Numbers to Improper Fractions
To subtract the mixed numbers, it is convenient to first convert them into improper fractions. For the bread:
\[3 \frac{1}{4} = \frac{3 \times 4 + 1}{4} = \frac{13}{4}.\]
For the cake:
\[2 \frac{2}{3} = \frac{2 \times 3 + 2}{3} = \frac{8}{3}.\]
Now, we have the expression \(\frac{13}{4} - \frac{8}{3}\).
- Calculating the Difference
To subtract these fractions, we need a common denominator. The least common multiple of 4 and 3 is 12. We convert each fraction:
\[\frac{13}{4} = \frac{13 \times 3}{4 \times 3} = \frac{39}{12},\]
\[\frac{8}{3} = \frac{8 \times 4}{3 \times 4} = \frac{32}{12}.\]
Now, we perform the subtraction:
\[\frac{39}{12} - \frac{32}{12} = \frac{39 - 32}{12} = \frac{7}{12}.\]
Thus, Cho used \(\frac{7}{12}\) more cups of flour for the bread than for the cake.
- Final Conclusion
Comparing our result to the given options, we find that the difference is \(\frac{7}{12}\) cup. The final answer is \(\boxed{\frac{7}{12}}\).
Examples
Understanding how to subtract mixed fractions is essential in everyday life, particularly in cooking and baking. For example, if a recipe calls for \(1 \frac{1}{2}\) cups of sugar but you only have \(1 \frac{1}{4}\) cups, you can quickly determine you are missing \(\frac{1}{4}\) cup. Mastering these conversions and operations helps you adjust ingredients accurately, ensuring your culinary projects turn out perfectly every time.