1. **State the problem:** Carlos has 4 tennis balls and 5 baseballs, making a total of 9 balls. We need to find fractions and comparisons of these quantities. 2. **Total number of balls:** $$4 + 5 = 9$$ 3. **a. Fraction of tennis balls:** The fraction of tennis balls to total balls is given by: $$\frac{\text{number of tennis balls}}{\text{total balls}} = \frac{4}{9}$$ 4. **b. Fraction of baseballs:** Similarly, the fraction of baseballs to total balls is: $$\frac{5}{9}$$ 5. **c. Numerical comparison of baseballs to total balls using words:** "5 to 9" 6. **d. Using colon notation to compare each type to total balls:** Tennis balls to total balls: $$4:9$$ Baseballs to total balls: $$5:9$$ 7. **e. Explanation of notations 4/9, 4 to 9, and 4:9:** All three notations represent the ratio of tennis balls to total balls. The fraction $$\frac{4}{9}$$ shows the part over whole as a fraction. "4 to 9" and "4:9" are different ways to express the same ratio numerically, with "to" as a word and ":" as a symbol. **Final answers:** a. $$\frac{4}{9}$$ b. $$\frac{5}{9}$$ c. "5 to 9" d. Tennis balls to total: $$4:9$$, Baseballs to total: $$5:9$$ e. All notations express the ratio of tennis balls to total balls in different formats.