1. **Problem:** Racheal bought $\frac{2}{5}$ metre of ribbon and Latifat bought $\frac{3}{4}$ metre of ribbon. Find the total length of the ribbon they bought. 2. **Formula:** To add fractions, use $$\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}$$ where $a,b,c,d$ are integers and $b,d \neq 0$. 3. **Step-by-step solution:** - Add $\frac{2}{5}$ and $\frac{3}{4}$: $$\frac{2}{5} + \frac{3}{4} = \frac{2 \times 4}{5 \times 4} + \frac{3 \times 5}{4 \times 5} = \frac{8}{20} + \frac{15}{20}$$ - Combine the fractions: $$\frac{8}{20} + \frac{15}{20} = \frac{8 + 15}{20} = \frac{23}{20}$$ - Simplify the improper fraction to a mixed number: $$\frac{23}{20} = 1 \frac{3}{20}$$ 4. **Explanation:** We found a common denominator (20) to add the fractions easily. Then, we added the numerators and kept the denominator the same. Finally, we converted the improper fraction to a mixed number for easier interpretation. **Final answer:** The total length of the ribbon they bought is $1 \frac{3}{20}$ metres.