From the information given in the statement, you know that the baker is going to use 11 cups to prepare his cookies, because
![15\text{ cups of flour}-4\text{ cups of flour set aside }=11\text{ cups of flour}](https://img.qammunity.org/2023/formulas/mathematics/college/7zwat3xgycrtftb7ecs2qn4777mfjk7old.png)
Now, to find out how many batches of cookies the baker can make with 11 cups of flour, you can use the following ratio:
![\begin{gathered} \frac{1\text{ batch}}{(1)/(2)\text{ cup of flour}}=\frac{x\text{ batches}}{11\text{ cups of flour}} \\ \text{ Multiply by 11 cups of flour on both sides of the equation} \\ \frac{1\text{ batch}}{(1)/(2)\text{ cup of flour}}\cdot\text{11 cups of flour}=\frac{x\text{ batches}}{11\text{ cups of flour}}\cdot\text{11 cups of flour} \\ \frac{1\text{ batch}\cdot11\text{ cups of flour}}{(1)/(2)\text{ cup of flour}}=x \\ (1\cdot11)/((1)/(2))\text{ batches }=x \\ (11)/((1)/(2))\text{ batches = x} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/dsiqqklya3uiqz26xyqalrhkhunne112nk.png)
Since
![11=(11)/(1)](https://img.qammunity.org/2023/formulas/mathematics/college/i83tkvgel40xiyt2br8kk12pkl99xvy8gy.png)
then when dividing the fractions you have
![\begin{gathered} (11)/((1)/(2))\text{batches }=x \\ ((11)/(1))/((1)/(2))\text{batches }=x \\ (11\cdot2)/(1\cdot1)\text{batches }=x \\ (22)/(1)\text{batches }=x \\ 22\text{batches }=x \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/4myx164ubmtb48z4yaqq9ec3pygnyg93bg.png)
Therefore, the baker can make 22 cookie batches with 11 cups of flour.