NCERT Class 8 Mathematics Ganita Prakash Part-II: Chapter 3 — Proportional Reasoning-2
This chapter, "Proportionality — A Quick Recap," from NCERT's Class 8 Mathematics Ganita Prakash Part-II, revisits the concept of proportional relationships between quantities. It explains that when related quantities change by the same factor, their relationship is proportional. The chapter uses the example of idli batter preparation, where the ratio of rice to urad dal (e.g., 2:1) defines the proportion. It illustrates how to verify proportionality between two ratios (a:b and c:d) using the cross-multiplication method (a × d = b × c). The text also introduces the concept of Representative Fraction (RF) used in maps, explaining that a ratio like 1:60,00,000 signifies the relationship between a distance on the map and the actual ground distance, encouraging students to apply these concepts to real-world map measurements. This chapter reinforces foundational mathematical reasoning skills essential for CBSE curriculum.
Quick info
| Board | CBSE / NCERT |
|---|---|
| Class | Class 8 |
| Subject | Mathematics |
| Book | Ganita Prakash Part-II |
| Chapter | Chapter 3 — Proportional Reasoning-2 |
| Language | English |
| PDF type | NCERT Textbook |
| Session | CBSE 2026 |
| Reading time | 3 minutes |
| Word count | 448 |
Learning outcomes
- Understand and define proportional relationships between quantities.
- Represent proportional relationships using ratio notation.
- Verify proportionality of ratios using the cross-multiplication method.
- Understand the concept and application of Representative Fraction (RF) in maps.
- Calculate actual geographical distances from map distances using RF.
Vocabulary
| Word | Meaning |
|---|---|
| Proportional relationship | A relationship where quantities change by the same factor. |
| Ratio notation | A way to represent relationships between quantities, e.g., a: b. |
| Cross-multiplication | A method to verify proportionality: a × d = b × c for ratios a:b and c:d. |
| Representative Fraction (RF) | The ratio between a distance on a map and the corresponding actual distance on the ground. |
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Practice questions
- Are the ratios 3:4 and 6:8 proportional? Explain using cross-multiplication. Answer: Yes, 3 × 8 = 24 and 4 × 6 = 24. Since the products are equal, the ratios are proportional.
- If a map has an RF of 1:10,000, what is the actual distance on the ground for 5 cm on the map? Answer: 5 cm on the map represents 5 × 10,000 = 50,000 cm on the ground.
- Convert 50,000 cm to meters. Answer: 50,000 cm = 500 meters.
Frequently asked questions
What is a proportional relationship?
A proportional relationship exists between two or more quantities when they change by the same factor.
How can we verify if two ratios are proportional?
Two ratios a:b and c:d are proportional if a × d = b × c (cross-multiplication).
What does the Representative Fraction (RF) on a map mean?
RF shows the ratio between a distance on the map and the corresponding actual distance on the ground, e.g., 1:60,00,000 means 1 cm on map equals 60,00,000 cm on ground.
Is the RF on a map the same as road distance?
No, the RF represents geographical distance, not necessarily the actual road distance.
How do you convert map distance to actual distance using RF?
Multiply the map distance by the second number in the RF ratio (the 'ground' part).
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NCERT Class 8 Mathematics — Ganita Prakash Part-II — Chapter 3 — Proportional Reasoning-2. Verified by NCERT Help Editorial Team. Reviewed on 29 Jul 2026. Last updated 10 Aug 2026.