To find out how many servings of orange juice are in the container, we need to divide the total amount of orange juice by the size of one serving.
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Convert the total volume of orange juice from a mixed number to an improper fraction:
- \( 5 \frac{1}{3} \) cups can be converted as follows: \[ 5 \frac{1}{3} = \frac{5 \times 3 + 1}{3} = \frac{15 + 1}{3} = \frac{16}{3} \text{ cups} \]
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Determine the size of one serving:
- One serving is \( \frac{7}{8} \) of a cup.
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Divide the total volume of juice by the size of one serving: \[ \text{Number of servings} = \frac{\frac{16}{3}}{\frac{7}{8}} \]
To divide fractions, you multiply by the reciprocal: \[ \frac{16}{3} \times \frac{8}{7} = \frac{16 \times 8}{3 \times 7} = \frac{128}{21} \]
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Convert \( \frac{128}{21} \) to a mixed number:
- Divide 128 by 21 to find how many whole servings are there.
- 21 goes into 128 six times because \( 21 \times 6 = 126\).
- The remainder is \( 128 - 126 = 2 \).
Therefore, \[ \frac{128}{21} = 6 \frac{2}{21} \]
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To find the nearest whole serving:
- \( 6 \frac{2}{21} \) is closer to 6 than to 7.
So, the number of servings in the container, rounded to the nearest whole serving, is 6 servings.