9. Fraction Case Studies: Recipes, Shopping, Schedules, and Measurement

Fractions become real when they measure things.

Case study 1 - recipe scaling. A recipe uses \(\frac{2}{3}\) cup of milk for one batch. You need \(2\frac{1}{2}\) batches:
\[ \frac{2}{3}\times 2\frac{1}{2}=\frac{2}{3}\times\frac{5}{2}=\frac{10}{6}=\frac{5}{3}=1\frac{2}{3}. \]
You need \(1\frac{2}{3}\) cups of milk.

Case study 2 - shopping discount. A jacket is \(\frac{1}{4}\) off. That means you pay \(\frac{3}{4}\) of the price. If the original price is 80 dollars:
\[ \frac{3}{4}\times 80=60. \]

Case study 3 - schedule. A student studies \(\frac{3}{5}\) hour on Monday and \(\frac{7}{10}\) hour on Tuesday:
\[ \frac{3}{5}+\frac{7}{10}=\frac{6}{10}+\frac{7}{10}=\frac{13}{10}=1\frac{3}{10}. \]
Total study time is \(1\frac{3}{10}\) hours.

Case study 4 - measurement. A shelf is \(6\frac{1}{4}\) feet long. Each section is \(1\frac{1}{4}\) feet:
\[ 6\frac{1}{4}\div1\frac{1}{4}=\frac{25}{4}\div\frac{5}{4}=\frac{25}{4}\times\frac{4}{5}=5. \]
The shelf has 5 sections.