1. **Stating the problem:** A teacher noticed that $\frac{7}{12}$ of the students were wearing either blue shorts or white shorts. We need to write two different ways this could be done. 2. **Understanding the problem:** The fraction $\frac{7}{12}$ represents the combined portion of students wearing blue or white shorts. We want to express this as the sum of two fractions that add up to $\frac{7}{12}$. 3. **Formula and rules:** If $\frac{a}{b}$ and $\frac{c}{d}$ are fractions representing the parts of students wearing blue and white shorts respectively, then: $$\frac{a}{b} + \frac{c}{d} = \frac{7}{12}$$ where the denominators $b$ and $d$ should be compatible or converted to a common denominator. 4. **First way:** Let’s say $\frac{3}{12}$ wear blue shorts and $\frac{4}{12}$ wear white shorts. $$\frac{3}{12} + \frac{4}{12} = \frac{3+4}{12} = \frac{7}{12}$$ 5. **Second way:** Let’s say $\frac{1}{4}$ wear blue shorts and $\frac{5}{12}$ wear white shorts. First, convert $\frac{1}{4}$ to twelfths: $$\frac{1}{4} = \frac{3}{12}$$ Then add: $$\frac{3}{12} + \frac{5}{12} = \frac{8}{12}$$ This is more than $\frac{7}{12}$, so adjust the second fraction to $\frac{4}{12}$: $$\frac{3}{12} + \frac{4}{12} = \frac{7}{12}$$ Alternatively, use $\frac{2}{12}$ and $\frac{5}{12}$: $$\frac{2}{12} + \frac{5}{12} = \frac{7}{12}$$ 6. **Summary:** Two different ways to write $\frac{7}{12}$ as a sum of two fractions are: - $\frac{3}{12} + \frac{4}{12}$ - $\frac{2}{12} + \frac{5}{12}$ These represent different distributions of students wearing blue and white shorts.