Final answer:
The ratio of sugar to flour is 1/2:2/3, and when simplified, the value of the ratio is 2/3. This means the amount of sugar in the recipe is two-thirds of the amount of flour.
Step-by-step explanation:
The ratio of sugar to flour as the recipe calls for ⅓ cup of flour for every ½ cup sugar can be written as the fraction ½:⅓. To make this ratio easier to understand, we should express each quantity with the same denominator so they can be compared directly. To find a common denominator, we can convert ½ to 2/4 and ⅓ to 3/4. Now, our sugar to flour ratio is 2/4:3/4.
To find the value of this ratio, we can divide the numerator of the sugar amount by the numerator of the flour amount, which gives us 2/3. This represents the unit rate or the amount of sugar per unit of flour. The interpretation is that for every 3 parts of flour, we need 2 parts of sugar in the recipe.
Therefore, the amount of sugar in the recipe is ⅓ of the amount of flour. This allows us to efficiently scale the recipe up or down based on the available ingredients while maintaining the correct proportions.