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Francine uses (2)/(3) cup of pineapple juice for every (1)/(3) cup of orange juice to make a smoothie.
Enter the number of cups of pineapple juice Francine uses for 1 cup of orange juice.

◻ cups of pineapple juice

Francine uses 23\frac{2}{3} cup of pineapple juice for every 13\frac{1}{3} cup of orange juice to make a smoothie. \newlineEnter the number of cups of pineapple juice Francine uses for 11 cup of orange juice.\newline\square cups of pineapple juice

Full solution

Q. Francine uses 23\frac{2}{3} cup of pineapple juice for every 13\frac{1}{3} cup of orange juice to make a smoothie. \newlineEnter the number of cups of pineapple juice Francine uses for 11 cup of orange juice.\newline\square cups of pineapple juice
  1. Calculate pineapple to orange ratio: She uses (23)(\frac{2}{3}) cups of pineapple for every (13)(\frac{1}{3}) cup of orange juice, so we need to find out how many (23)(\frac{2}{3}) are in 11 cup.
  2. Divide 11 cup by orange juice amount: To do this, we divide 11 cup by the amount of orange juice she uses, which is (1)/(3)(1)/(3) cup: 1÷(1)/(3)1 \div (1)/(3).
  3. Multiply by reciprocal: Dividing by a fraction is the same as multiplying by its reciprocal, so we multiply 11 by the reciprocal of 13\frac{1}{3}, which is 33: 1×3=31 \times 3 = 3.
  4. Determine pineapple juice for 11 cup: Now we know she uses 33 times the amount of pineapple juice as she does orange juice for 11 cup of orange juice.
  5. Multiply pineapple amount by 33: So, we multiply the (23)(\frac{2}{3}) cups of pineapple juice by 33 to find out how much pineapple juice she uses for 11 cup of orange juice: (23)×3(\frac{2}{3}) \times 3.
  6. Final result: (23)×3=2×1=2(\frac{2}{3}) \times 3 = 2 \times 1 = 2 cups of pineapple juice.

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