Danielle bought 196 cups of flowers. She is making cakes for a large party. She needs 3.5 cups of flour for each cake. How many cakes can she make?

To find the number of cakes Danielle can make, divide the total number of cups of flowers by the number of cups of flour needed per cake: 196 cups / 3.5 cups/cake = <<196/3.5=56>>56 cakes. Answer: \boxed{56}.