From the information given in the statement, you know that the baker is going to use 11 cups to prepare his cookies, because
[tex]15\text{ cups of flour}-4\text{ cups of flour set aside }=11\text{ cups of flour}[/tex]Now, to find out how many batches of cookies the baker can make with 11 cups of flour, you can use the following ratio:
[tex]\begin{gathered} \frac{1\text{ batch}}{\frac{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}}{\frac{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}}{\frac{1}{2}\text{ cup of flour}}=x \\ \frac{1\cdot11}{\frac{1}{2}}\text{ batches }=x \\ \frac{11}{\frac{1}{2}}\text{ batches = x} \end{gathered}[/tex]Since
[tex]11=\frac{11}{1}[/tex]then when dividing the fractions you have
[tex]\begin{gathered} \frac{11}{\frac{1}{2}}\text{batches }=x \\ \frac{\frac{11}{1}}{\frac{1}{2}}\text{batches }=x \\ \frac{11\cdot2}{1\cdot1}\text{batches }=x \\ \frac{22}{1}\text{batches }=x \\ 22\text{batches }=x \end{gathered}[/tex]Therefore, the baker can make 22 cookie batches with 11 cups of flour.
