To solve how much more flour Cho used to bake the loaf of bread than to bake the cake, we need to perform some operations with fractions. Let’s break it down step-by-step.
1. First, convert the mixed numbers to improper fractions:
- For the cake: [tex]\( 2 \frac{2}{3} \)[/tex]
Convert [tex]\( 2 \frac{2}{3} \)[/tex] to an improper fraction:
[tex]\[
2 \frac{2}{3} = 2 + \frac{2}{3} = \frac{6}{3} + \frac{2}{3} = \frac{8}{3}
\][/tex]
- For the bread: [tex]\( 3 \frac{1}{4} \)[/tex]
Convert [tex]\( 3 \frac{1}{4} \)[/tex] to an improper fraction:
[tex]\[
3 \frac{1}{4} = 3 + \frac{1}{4} = \frac{12}{4} + \frac{1}{4} = \frac{13}{4}
\][/tex]
2. Calculate the difference between the two amounts of flour:
- The improper fractions we have are [tex]\( \frac{8}{3} \)[/tex] (cake) and [tex]\( \frac{13}{4} \)[/tex] (bread).
To subtract these fractions, we need a common denominator. The least common multiple of 3 and 4 is 12.
- Convert both fractions to have the common denominator of 12:
[tex]\[
\frac{8}{3} \times \frac{4}{4} = \frac{32}{12}
\][/tex]
[tex]\[
\frac{13}{4} \times \frac{3}{3} = \frac{39}{12}
\][/tex]
- Subtract the fractions:
[tex]\[
\frac{39}{12} - \frac{32}{12} = \frac{7}{12}
\][/tex]
3. Convert the result back into a mixed number if necessary. In this case, [tex]\( \frac{7}{12} \)[/tex] is already in its simplest form.
Cho used [tex]\( \frac{7}{12} \)[/tex] cups more flour to bake the loaf of bread than the cake.
So, the correct answer is:
[tex]\[
\frac{7}{12} \text{ cup}
\][/tex]
