You mix (2)/(3) teaspoon of baking soda with 3 teaspoons of salt. Find and interpret the value of the ratio of baking soda to salt. The value of the ratio is The amount of baking soda is the amount of salt
The Correct Answer and Explanation is:
The value of the ratio of baking soda to salt is found by comparing the two quantities directly:
[
\text{Ratio of baking soda to salt} = \frac{\frac{2}{3} \text{ teaspoon of baking soda}}{3 \text{ teaspoons of salt}}
]
To simplify this ratio:
[
\frac{\frac{2}{3}}{3} = \frac{2}{3} \times \frac{1}{3} = \frac{2}{9}
]
Thus, the ratio of baking soda to salt is ( \frac{2}{9} ).
Interpretation of the Ratio
The ratio ( \frac{2}{9} ) means that for every 9 parts of the mixture, 2 parts are baking soda, and the remaining 7 parts are salt. This ratio provides a way to understand the relative amounts of each ingredient in the mixture.
Practical Example:
Imagine that you are preparing a recipe where you mix baking soda and salt. If the total amount of salt used is 3 teaspoons, you are using only ( \frac{2}{3} ) teaspoon of baking soda. The ratio of ( \frac{2}{9} ) illustrates that baking soda is much less present compared to salt—specifically, there is only about 22% as much baking soda as there is salt in the mixture.
Usage in Proportional Relationships:
Ratios like ( \frac{2}{9} ) are important when scaling up or down a recipe. For instance, if you wanted to double the mixture, you would multiply both the baking soda and salt amounts by the same factor, maintaining the ( \frac{2}{9} ) ratio. So, if you used 6 teaspoons of salt, you would need ( 6 \times \frac{2}{9} = \frac{12}{9} = \frac{4}{3} ) teaspoons of baking soda.
In summary, the ratio ( \frac{2}{9} ) describes how much smaller the amount of baking soda is compared to salt, and it helps maintain consistent proportions in recipes.