1. Statement of the problem: We will solve a test problem involving fractions, area, and ratios suitable for Year 8 IGCSE level. 2. Problem example: If the ratio of the lengths of two rectangles is $3:4$ and their widths are equal, find the ratio of their areas. 3. Step 1: Let the common width be $w$. 4. Step 2: Let the length of the first rectangle be $3x$ and the second be $4x$ for some positive $x$. 5. Step 3: Area of first rectangle $= 3x \times w = 3xw$. 6. Step 4: Area of second rectangle $= 4x \times w = 4xw$. 7. Step 5: Ratio of areas $= \frac{3xw}{4xw} = \frac{3}{4}$. 8. Conclusion: The ratio of their areas is $3:4$. This demonstrates that when widths are equal, the ratio of lengths directly gives the ratio of areas.