A recipe calls for 1/2 cup of water for every 3/4 cup of flour. How much water is needed to mix with 1 cup of flour?

1. Start with the given ratio:
\frac{1}{2} \ : \ \frac{3}{4}
2. Set up the proportion with \( x \) representing the unknown amount of water for 1 cup of flour:
\frac{1}{2} \ : \ \frac{3}{4} = x \ : 1
3. Cross-multiply to solve for \( x \):
\frac{1}{2} \times 1 = x \times \frac{3}{4}
4. Simplify the equation:
\frac{1}{2} = \frac{3}{4} x
5. Solve for \( x \):
x = \frac{1/2}{3/4} = \frac{1}{2} \times \frac{4}{3} = \frac{4}{6} = \frac{2}{3}

Therefore, the amount of water needed is

\frac{2}{3} \text{ cup of water}