1. **State the problem:** We have 15 blocks of butter and need to find how much butter is left after making three cakes with the following butter requirements: - First cake: 3 whole blocks and \frac{2}{3} of a block - Second cake: 5 whole blocks and \frac{4}{5} of a block - Third cake: 2 whole blocks 2. **Write the calculation using brackets:** $$15 - \left(3 + \frac{2}{3} + 5 + \frac{4}{5} + 2\right)$$ 3. **Write the calculation without brackets:** $$15 - 3 - \frac{2}{3} - 5 - \frac{4}{5} - 2$$ 4. **Which calculation is easier?** The calculation with brackets is easier because it groups all the amounts to subtract together, making it clear that we first find the total butter used and then subtract from 15. 5. **Calculate the amount of butter used:** First, add the whole numbers: $$3 + 5 + 2 = 10$$ Next, add the fractions: $$\frac{2}{3} + \frac{4}{5} = \frac{2 \times 5}{3 \times 5} + \frac{4 \times 3}{5 \times 3} = \frac{10}{15} + \frac{12}{15} = \frac{22}{15}$$ 6. **Convert \frac{22}{15} to a mixed number:** $$\frac{22}{15} = 1 \frac{7}{15}$$ 7. **Add the whole number and fraction parts:** $$10 + 1 \frac{7}{15} = 11 \frac{7}{15}$$ 8. **Calculate butter left:** $$15 - 11 \frac{7}{15} = 15 - \left(11 + \frac{7}{15}\right) = (15 - 11) - \frac{7}{15} = 4 - \frac{7}{15}$$ 9. **Subtract the fraction from 4:** $$4 = \frac{60}{15}$$ $$\frac{60}{15} - \frac{7}{15} = \frac{53}{15}$$ 10. **Convert \frac{53}{15} to a mixed number:** $$\frac{53}{15} = 3 \frac{8}{15}$$ **Final answer:** The company will have \boxed{3 \frac{8}{15}} blocks of butter left after making all three cakes.