A tablespoon is equivalent to about 4 teaspoons. A recipe calls for 2/3 cup of sugar for every 1/2 teaspoon vanilla. What is the unit rate in tablespoons per cup?
I understand the exercise is about unit rates, but why go out of the way to state false information? A tablespoon is exactly 3 teaspoons!
Anyway,
(1/2 tsp)/(2/3 cup) * (1tbsp)/(4tsp) = 1/2 * 3/2 * 1/4 = 3/16 tbsp/cup
To find the unit rate in tablespoons per cup, we need to first convert the given measurements of tablespoons and cups to a common unit. In this case, we will convert both tablespoons and cups to teaspoons.
We know that 1 tablespoon is equivalent to 4 teaspoons. And since there are 16 tablespoons in a cup, we can calculate how many teaspoons are in a cup:
16 tablespoons * 4 teaspoons/tablespoon = 64 teaspoons
So, 1 cup is equal to 64 teaspoons.
Now, let's calculate the teaspoons of sugar per cup, using the given ratio:
2/3 cup of sugar for every 1/2 teaspoon of vanilla
We can multiply both sides of this ratio by 3/2 to get the equivalent ratio in terms of teaspoons:
(2/3 cup) * (3/2) = (2/2) teaspoons
(2/2) teaspoons = 1 teaspoon
So, there is 1 teaspoon of sugar for every 1 teaspoon of vanilla.
To calculate the unit rate in tablespoons per cup, we can find the ratio of teaspoons of sugar to cups:
(1 teaspoon of sugar) / (64 teaspoons of sugar) = 1/64
This means there is 1/64 cup of sugar per cup.
Since 1 tablespoon is equal to 4 teaspoons, we can multiply both sides by 4 to convert the ratio to tablespoons:
(1/64 cup of sugar) * (4 tablespoons/1 cup) = 1/16 tablespoon
So, the unit rate is 1/16 tablespoon per cup.