Question
The container of orange juice held 5 and one-third cups of juice. If a serving of orange juice is StartFraction 7 Over 8 EndFraction of a cup of orange juice, to the nearest whole serving, how many servings were in the container?
Answers
GPT-4o mini
To determine how many servings are in the container that holds \( 5 \frac{1}{3} \) cups of orange juice, we first need to convert \( 5 \frac{1}{3} \) into an improper fraction.
1. Convert \( 5 \frac{1}{3} \) into an improper fraction:
\[
5 \frac{1}{3} = \frac{5 \times 3 + 1}{3} = \frac{15 + 1}{3} = \frac{16}{3} \text{ cups}
\]
2. Now, calculate the number of servings by dividing the total amount of juice by the serving size:
\[
\text{Serving size} = \frac{7}{8} \text{ cup}
\]
\[
\text{Number of servings} = \frac{\frac{16}{3}}{\frac{7}{8}} = \frac{16}{3} \times \frac{8}{7}
\]
3. Multiply the fractions:
\[
\frac{16 \times 8}{3 \times 7} = \frac{128}{21}
\]
4. Now, calculate \( \frac{128}{21} \) to find the number of servings:
\[
\frac{128}{21} \approx 6.0952
\]
5. Finally, rounding to the nearest whole number:
\[
6.0952 \text{ rounds to } 6
\]
Thus, the container holds approximately **6 servings** of orange juice.
1. Convert \( 5 \frac{1}{3} \) into an improper fraction:
\[
5 \frac{1}{3} = \frac{5 \times 3 + 1}{3} = \frac{15 + 1}{3} = \frac{16}{3} \text{ cups}
\]
2. Now, calculate the number of servings by dividing the total amount of juice by the serving size:
\[
\text{Serving size} = \frac{7}{8} \text{ cup}
\]
\[
\text{Number of servings} = \frac{\frac{16}{3}}{\frac{7}{8}} = \frac{16}{3} \times \frac{8}{7}
\]
3. Multiply the fractions:
\[
\frac{16 \times 8}{3 \times 7} = \frac{128}{21}
\]
4. Now, calculate \( \frac{128}{21} \) to find the number of servings:
\[
\frac{128}{21} \approx 6.0952
\]
5. Finally, rounding to the nearest whole number:
\[
6.0952 \text{ rounds to } 6
\]
Thus, the container holds approximately **6 servings** of orange juice.