Let's break down the problem of determining how much water you'll need for 8 cups of flour, given that the recipe originally calls for 3 cups of flour for every [tex]\(\frac{1}{3}\)[/tex] cup of water.
1. Identify the Known Quantities:
- The recipe calls for 3 cups of flour.
- The corresponding amount of water is [tex]\(\frac{1}{3}\)[/tex] cup.
2. Determine the Ratio of Water to Flour:
- We can find the ratio of water to flour by using the given quantities:
[tex]\[
\text{Ratio of water to flour} = \frac{\text{Cups of water}}{\text{Cups of flour}} = \frac{\frac{1}{3}}{3}
\][/tex]
- Simplifying this:
[tex]\[
\frac{\frac{1}{3}}{3} = \frac{1}{3} \times \frac{1}{3} = \frac{1}{9}
\][/tex]
- So the ratio of water to flour is [tex]\(\frac{1}{9}\)[/tex].
3. Apply the Ratio to the New Quantity of Flour:
- Given that we need 8 cups of flour, we use the ratio to find the corresponding amount of water:
[tex]\[
\text{Cups of water needed} = \frac{1}{9} \times 8 = \frac{8}{9}
\][/tex]
- Thus, for 8 cups of flour, the amount of water needed is [tex]\(\frac{8}{9}\)[/tex] cups.
So, summarizing the steps and result:
- We first identified the ratio of water to flour as [tex]\(\frac{1}{9}\)[/tex].
- Using this ratio, for 8 cups of flour, we calculated the amount of water needed to be [tex]\(\frac{8}{9}\)[/tex] cups.
Therefore, for 8 cups of flour, you will need [tex]\(\frac{8}{9}\)[/tex] cups, or approximately 0.8889 cups of water.
