1. The problem asks us to fill in the blanks in the equation $$10 + 35 = 5 \times (\_ + \_)$$ so that both sides are equal. 2. First, simplify the left side: $$10 + 35 = 45$$ 3. The right side is $$5 \times (a + b)$$ where $$a$$ and $$b$$ are the numbers to find. 4. Since $$5 \times (a + b) = 45$$, divide both sides by 5: $$\frac{45}{5} = a + b$$ 5. Simplify the division: $$\cancel{\frac{45}{5}} = 9 = a + b$$ 6. So, the sum inside the parentheses must be 9. There are many pairs of numbers that add to 9, for example, 4 and 5. 7. Therefore, one correct answer is: $$10 + 35 = 5 \times (4 + 5)$$ This satisfies the equation because $$5 \times 9 = 45$$. Final answer: The numbers to fill in are 4 and 5.