To find out how many cups of water you need for 9 cups of flour, you can set up a proportion based on the initial recipe.
The original ratio from the recipe is:
- 2 cups of flour requires 4.5 cups of water (since 4 1/2 cups can be expressed as 4.5).
Let's set this up in a table format:
| Cups of Flour | Cups of Water | |---------------|---------------| | 2 | 4.5 | | 4 | 9.0 | | 9 | ? |
To find the amount of water needed for 9 cups of flour, we can set up a proportion based on the known quantities:
\[ \frac{2 \text{ cups flour}}{4.5 \text{ cups water}} = \frac{9 \text{ cups flour}}{x \text{ cups water}} \]
Cross-multiplying to solve for \( x \):
\[ 2x = 9 \cdot 4.5 \]
Calculating \( 9 \cdot 4.5 \):
\[ 9 \cdot 4.5 = 40.5 \]
So we have:
\[ 2x = 40.5 \]
Now, divide both sides by 2:
\[ x = \frac{40.5}{2} = 20.25 \]
Therefore, for 9 cups of flour, you will need 20.25 cups of water.
Now, filling in the table:
| Cups of Flour | Cups of Water | |---------------|---------------| | 2 | 4.5 | | 4 | 9.0 | | 9 | 20.25 |
To enter the answer as a fraction, you can express 20.25 as \( \frac{81}{4} \) (since 20.25 = 20 + 0.25 = 20 + \frac{1}{4} = \frac{80}{4} + \frac{1}{4} = \frac{81}{4}).
Thus, the answer for the amount of water needed for 9 cups of flour is \( \frac{81}{4} \) cups of water.