a)
well, we know the batch uses 3¼, and she has 10½, so
how many times does 3¼ go into 10½?
again, let's firstly convert the mixed fractions to improper fractions, and then divide.
[tex]\bf \stackrel{mixed}{10\frac{1}{2}}\implies \cfrac{10\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{21}{2}}~\hfill \stackrel{mixed}{3\frac{1}{4}}\implies \cfrac{3\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{13}{4}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{~~\frac{21}{2}~~}{\frac{13}{4}}\implies \cfrac{21}{2}\cdot \cfrac{4}{13}\implies \cfrac{21}{13}\cdot \cfrac{4}{2}\implies \cfrac{21}{13}\cdot 2\implies \cfrac{42}{13}\implies 3\frac{3}{13}[/tex]
nevermind the 3/13 part, only 3 whole batches.
b)
[tex]\bf \stackrel{\textit{one batch}}{3\frac{1}{4}}\qquad \stackrel{\textit{5 batches}}{3\frac{1}{4}+3\frac{1}{4}+3\frac{1}{4}+3\frac{1}{4}+3\frac{1}{4}}\implies \cfrac{13}{4}+\cfrac{13}{4}+\cfrac{13}{4}+\cfrac{13}{4}+\cfrac{13}{4} \\\\\\ \textit{or just}\qquad 5\cdot \cfrac{13}{4}\implies \cfrac{65}{4}\implies 16\frac{1}{4}[/tex]
