1. The problem involves understanding and comparing ratios in different forms: part-to-part, part-to-whole, and whole-to-part. 2. Ratios compare quantities and can be written as fractions or with the word "to". For example, "4 to 5" means the ratio of 4 parts to 5 parts, which can be written as $\frac{4}{5}$. 3. Let's analyze the first ratio given: tennis balls to baseballs is 4 to 5. 4. Writing this ratio as a fraction: $$\frac{4}{5}$$ means for every 4 tennis balls, there are 5 baseballs. 5. The inequality $4 \text{ to } 5 < \frac{4}{5} < \frac{5}{4}$ means the ratio 4 to 5 is less than $\frac{4}{5}$, which is less than $\frac{5}{4}$. This shows the relationship between the ratio and its reciprocal. 6. Similarly, baseballs to tennis balls is 5 to 4, which is the reciprocal of tennis balls to baseballs. 7. For part-to-whole ratios, tennis balls to total balls is 4 to 9, written as $\frac{4}{9}$, meaning tennis balls make up 4 parts out of 9 total parts. 8. Baseballs to total balls is 5 to 9, or $\frac{5}{9}$. 9. Whole-to-part ratios invert the part-to-whole ratios. For example, total balls to tennis balls is 9 to 4, or $\frac{9}{4}$. 10. Understanding these ratios helps compare quantities in different contexts. Final answer: The ratios are correctly expressed and compared as fractions and inequalities, showing the relationships between parts and wholes.