1. **State the problem:** Calculate the following expressions involving Fibonacci numbers $F_n$: (a) $F_3 + F_4 + F_5 + F_6 + F_7$ (b) $F_3 + 4 + 5 + 6 + 7$ (c) $F_5 \times F_7$ (d) $F_5 \times 7$ 2. **Recall Fibonacci numbers:** The Fibonacci sequence is defined as $F_1=1$, $F_2=1$, and $F_n=F_{n-1}+F_{n-2}$ for $n>2$. The first few Fibonacci numbers are: $$F_1=1, F_2=1, F_3=2, F_4=3, F_5=5, F_6=8, F_7=13$$ 3. **Calculate each part:** (a) Sum of Fibonacci numbers: $$F_3 + F_4 + F_5 + F_6 + F_7 = 2 + 3 + 5 + 8 + 13$$ $$= 31$$ (b) Sum of $F_3$ and integers 4,5,6,7: $$F_3 + 4 + 5 + 6 + 7 = 2 + 4 + 5 + 6 + 7$$ $$= 24$$ (c) Product of Fibonacci numbers $F_5$ and $F_7$: $$F_5 \times F_7 = 5 \times 13$$ $$= 65$$ (d) Product of Fibonacci number $F_5$ and 7: $$F_5 \times 7 = 5 \times 7$$ $$= 35$$ 4. **Final answers:** (a) 31 (b) 24 (c) 65 (d) 35 All answers are integers, so no rounding is needed.