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?

5 servings
6 servings
15 servings
19 servings

1 answer

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.

  1. 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: \[ 5 \frac{1}{3} = \frac{5 \times 3 + 1}{3} = \frac{15 + 1}{3} = \frac{16}{3} \text{ cups} \]
  2. Determine the size of one serving:

    • One serving is \( \frac{7}{8} \) of a cup.
  3. 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: \[ \frac{16}{3} \times \frac{8}{7} = \frac{16 \times 8}{3 \times 7} = \frac{128}{21} \]

  4. 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, \[ \frac{128}{21} = 6 \frac{2}{21} \]

  5. 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.