A recipe calls for 2/3 cup of sugar for every 8/9 teaspoons of vanilla. The unit rate of sugar to vanilla is
2/3 : 8/9 = 6/9 : 8/9 = 6:8 = 3:4
To find the unit rate of sugar to vanilla, we can divide the amount of sugar by the amount of vanilla.
The recipe calls for 2/3 cup of sugar for every 8/9 teaspoons of vanilla.
First, let's convert the measurements to a common unit. Since 1 cup is equal to 48 teaspoons, we can convert the sugar measurement by multiplying 2/3 by 48/1:
2/3 * 48/1 = (2 * 48) / (3 * 1) = 96/3 = 32 teaspoons of sugar.
Now, we can find the unit rate by dividing the amount of sugar by the amount of vanilla:
32 teaspoons of sugar / 8/9 teaspoons of vanilla = 32 / (8/9) = 32 * (9/8) = 36.
Therefore, the unit rate of sugar to vanilla is 36.
To find the unit rate of sugar to vanilla, we need to determine how much sugar is needed for one teaspoon of vanilla.
The recipe states that for every 8/9 teaspoons of vanilla, 2/3 cup of sugar is required.
To find the unit rate, divide the amount of sugar (2/3 cup) by the amount of vanilla (8/9 teaspoons):
(2/3) ÷ (8/9)
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:
(2/3) * (9/8)
Multiplying across gives us:
(2 * 9) / (3 * 8)
Simplifying the fraction gives us:
18/24
This fraction can be further simplified by dividing both the numerator and denominator by their greatest common divisor, which is 6:
18/24 = 3/4
Therefore, the unit rate of sugar to vanilla is 3/4 cup of sugar per teaspoon of vanilla.