Let b be the number of batches that can be made with 9 cups of flour.
Since each batch requires 2 1/4 cups of flour, then for b batches, the amount of flour needed would be:
[tex]2\frac{1}{4}\times b[/tex]Then, the resulting equation for b is:
[tex]2\frac{1}{4}\times b=9[/tex]Divide both sides by 2 1/4 to find b:
[tex]\begin{gathered} 2\frac{1}{4}\times b\div2\frac{1}{4}=9\div2\frac{1}{4} \\ \Rightarrow b=9\div(2+\frac{1}{4}) \\ =9\div(\frac{9}{4}) \\ =4 \end{gathered}[/tex]Therefore, the answer is:
[tex]2\frac{1}{4}b=9;\text{ }b=4[/tex]