A punch recipe requires 2/5 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? in fraction form

Answer 1

To find the unit rate of soda to pineapple juice, we start with the given amounts in the recipe:

• Pineapple juice: \( \frac{2}{5} \) cup

• Soda: \( 2 \frac{1}{2} \) cups, which can be converted to an improper fraction as follows:

  \[ 2 \frac{1}{2} = 2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2} \text{ cups} \]

Now we can set up the ratio of soda to pineapple juice:

\[ \text{Ratio} = \frac{\text{soda}}{\text{pineapple juice}} = \frac{\frac{5}{2}}{\frac{2}{5}} \]

To simplify this ratio, we multiply by the reciprocal of the denominator:

\[ \frac{5}{2} \div \frac{2}{5} = \frac{5}{2} \times \frac{5}{2} = \frac{5 \times 5}{2 \times 2} = \frac{25}{4} \]

Thus, the ratio of soda to pineapple juice in fraction form is:

\[ \frac{25}{4} \]

So the unit rate of soda to pineapple juice in the punch is \( \frac{25}{4} \).