A punch recipe requires 3/5 of a cup of pineapple juice for every 2 1/2 cups of soda what is the unit rate of soda to pineapple juice in the punch
A. 6/25 cup of soda per cup of pineapple juice
B. 1 1/5 cups of soda per cup of pineapple juice
C. 8 1/3 cups of soda per cup of pineapple juice
D. 4 1/6 cups of soda per cup of pineapple juice
To find the unit rate of soda to pineapple juice, we need to divide the amount of soda by the amount of pineapple juice.
The recipe requires 2 1/2 cups of soda for every 3/5 cup of pineapple juice.
First, we need to change 2 1/2 cups to an improper fraction:
2 1/2 = 5/2 cups of soda
Next, we divide the amount of soda by the amount of pineapple juice:
(5/2) / (3/5) = (5/2) * (5/3) = 25/6
Thus, the unit rate of soda to pineapple juice in the punch is 25/6 cups of soda per cup of pineapple juice.
Simplifying this fraction, we get:
25/6 = 4 1/6
Therefore, the correct answer is D. 4 1/6 cups of soda per cup of pineapple juice.
To find the unit rate of soda to pineapple juice in the punch, we need to divide the amount of soda by the amount of pineapple juice.
Given that the recipe requires 2 1/2 cups of soda for every 3/5 of a cup of pineapple juice, we can divide 2 1/2 by 3/5.
To divide a fraction by a fraction, we invert the divisor (the second fraction) and multiply.
2 1/2 ÷ 3/5 = 5/2 ÷ 3/5
When dividing fractions, we multiply the numerator by the reciprocal of the divisor.
5/2 × 5/3 = (5 × 5) ÷ (2 × 3) = 25/6
So, the unit rate of soda to pineapple juice in the punch is 25/6 cups of soda per cup of pineapple juice.
But we need to simplify the fraction.
The simplified fraction of 25/6 is 4 1/6.
Therefore, the correct option is D. 4 1/6 cups of soda per cup of pineapple juice.
To find the unit rate of soda to pineapple juice in the punch recipe, we need to determine the amount of soda for every 1 cup of pineapple juice.
The recipe requires 3/5 cup of pineapple juice for every 2 1/2 cups of soda.
First, let's convert 2 1/2 cups to a common fraction:
2 + 1/2 = 5/2
Now, we can set up a ratio of pineapple juice to soda:
(3/5) / (5/2)
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:
(3/5) * (2/5)
Multiplying fractions, we get:
6/25
Therefore, the unit rate of soda to pineapple juice in the punch is 6/25 cup of soda per cup of pineapple juice.
So, option A is the correct answer: 6/25 cup of soda per cup of pineapple juice.