1. **Stating the problem:** We are given several fractions and mixed numbers: $\frac{1}{4}$, $7 \frac{1}{5}$, $2 \frac{1}{8}$, $\frac{2}{3}$, and $\frac{4}{9}$. The problem involves understanding these numbers, possibly converting mixed numbers to improper fractions, and comparing or using them in calculations. 2. **Formula and rules:** To work with mixed numbers and fractions, recall: - A mixed number $a \frac{b}{c}$ can be converted to an improper fraction by $\frac{a \times c + b}{c}$. - To compare or add fractions, convert them to a common denominator. 3. **Convert mixed numbers to improper fractions:** - $7 \frac{1}{5} = \frac{7 \times 5 + 1}{5} = \frac{35 + 1}{5} = \frac{36}{5}$ - $2 \frac{1}{8} = \frac{2 \times 8 + 1}{8} = \frac{16 + 1}{8} = \frac{17}{8}$ 4. **List all fractions as improper fractions:** - $\frac{1}{4}$ (already a fraction) - $\frac{36}{5}$ - $\frac{17}{8}$ - $\frac{2}{3}$ - $\frac{4}{9}$ 5. **Explanation:** These fractions can be used for further operations such as addition, subtraction, or comparison. For example, to compare, find a common denominator or convert to decimals. 6. **Example comparison:** Convert to decimals: - $\frac{1}{4} = 0.25$ - $\frac{36}{5} = 7.2$ - $\frac{17}{8} = 2.125$ - $\frac{2}{3} \approx 0.6667$ - $\frac{4}{9} \approx 0.4444$ This shows the relative sizes of the numbers. **Final note:** The problem description mentions circles and rectangles with these fractions, likely a visual representation. The key math takeaway is converting mixed numbers to improper fractions and understanding fraction values.