To find out how many cups of flour are needed for one loaf of challah bread, we start with the amount of flour used to make 3 loaves, which is \(3 \frac{1}{2}\) cups.
First, convert \(3 \frac{1}{2}\) into an improper fraction:
\[ 3 \frac{1}{2} = \frac{7}{2} \text{ cups of flour} \]
Next, to find the flour needed for one loaf, divide the total amount of flour by the number of loaves, which is 3:
\[ \text{Flour for one loaf} = \frac{\frac{7}{2}}{3} = \frac{7}{2} \times \frac{1}{3} = \frac{7}{6} \]
Now, we can convert \(\frac{7}{6}\) into a mixed number:
\(\frac{7}{6}\) is equal to \(1 \frac{1}{6}\).
Thus, the amount of flour needed for one loaf of challah bread is 1 1/6 cups.
So, the answer is 1 1/6.