PROPORTIONAL 3 REASONING–2 | Class 8 Mathematics Notes

3.1 Proportionality—A Quick Recap

This section revisits the fundamental concept of proportionality introduced in earlier chapters. Proportionality describes a relationship between two or more quantities that change by the same factor, maintaining a constant ratio between them. For example, in cooking idli batter, the ratio of rice to urad dal is often 2:1, meaning for every 2 cups of rice, 1 cup of urad dal is added. This ratio can vary regionally but remains constant within a recipe to maintain taste. To check if two ratios are proportional, the cross-multiplication method is used: two ratios a:b and c:d are proportional if a × d = b × c. Alternatively, the equality of fractions a/c = b/d also confirms proportionality. For instance, Viswanath’s mixture of 6 cups rice to 3 cups urad dal (6:3) and Puneet’s mixture of 4 cups rice to 2 cups urad dal (4:2) are proportional because 6 × 2 = 3 × 4 = 12. This implies that if other ingredients are also in proportion, the idlis made by both would taste the same. This section lays the groundwork for understanding more complex proportional reasoning in the chapter.

📊 Diagram: See figure_1: The two products are the same (12). So, the two ratios are proportional. It is likely that the idlis would taste the same, if all the other ingredients are proportional too!

🧪 Activity: Students are encouraged to verify proportionality of different mixtures using cross-multiplication to understand the concept practically.

🔗 Connection: This section introduces the concept of proportionality, which leads naturally into understanding ratios in real-world contexts such as maps in the next section.