A recipe calls for 2/3 cup of sugar for every 2 teaspoons of vanilla. What is the unit rate in cups per teaspoon?
(2/3) / 2 = ?
To find the unit rate in cups per teaspoon, we need to determine how many cups of sugar are needed for every teaspoon of vanilla.
Given that the recipe calls for 2/3 cup of sugar for every 2 teaspoons of vanilla, we can set up a ratio:
2/3 cup of sugar : 2 teaspoons of vanilla
To make the ratio easier to work with, we can scale it up by multiplying both sides by 3:
(2/3) * 3 cups of sugar : 2 * 3 teaspoons of vanilla
(2/3) * 3 cups of sugar : 6 teaspoons of vanilla
Simplifying, we get:
2 cups of sugar : 6 teaspoons of vanilla
Now, to find the unit rate, we need to have a common unit on both sides of the ratio. Since we're looking for the rate in cups per teaspoon, we need to convert the teaspoons to cups.
There are 48 teaspoons in a cup, so we can set up another ratio:
2 cups of sugar : 6 teaspoons of vanilla
2 cups of sugar : 6/48 cups of vanilla
Simplifying the ratio, we get:
2 cups of sugar : 1/8 cup of vanilla
Therefore, the unit rate in cups per teaspoon is 1/8 cup.
To find the unit rate in cups per teaspoon, we need to divide the amount of sugar (in cups) by the amount of vanilla (in teaspoons).
The recipe calls for 2/3 cup of sugar for every 2 teaspoons of vanilla.
So, the unit rate is:
(2/3) cup / 2 teaspoons
To simplify this fraction, we can multiply the numerator and the denominator by 3:
(2/3) * (3/3) cup / 2 teaspoons = 2/9 cup / 2 teaspoons
Now, we can divide the numerator by the denominator:
2/9 cup ÷ 2 teaspoons = 1/9 cup per teaspoon
Therefore, the unit rate in cups per teaspoon is 1/9 cup per teaspoon.