NCERT Solutions for Ganita Prakash (Part 2) Chapter 3 Proportional Reasoning-2
Updated on 2026-09-05
About this chapter
Two ratios a : b and c : d are proportional when a × d = b × c. A ratio may have many terms: 8 : 4 : 2 : 1 says that whatever multiplies one term multiplies all of them. The RF (Representative Fraction) on a map, such as 1 : 60,00,000, is a ratio between two lengths, so it carries no unit — 1 cm on the map stands for 60,00,000 cm, that is 60 km, of straight-line ground distance. To divide a quantity x in the ratio a : b : c : …, add the terms and give each part its share: x × a/(a + b + c + …), x × b/(a + b + c + …), and so on. A pie chart divides 360° in the ratio of the data. Since 360° stands for the whole, each category gets an angle proportional to its count — one degree per person when 360 people are surveyed. Directly proportional quantities keep their quotient fixed: x₁/y₁ = x₂/y₂
- Proportionality
- Ratios in Maps
- Ratios with More than 2 Terms
- Dividing a Whole in a Given Ratio
- A Slice of the Pie
- Inverse Proportions
- –68Section 3.6 Inverse Proportions
Exercises
- In-text Questions — Proportionality Page 55
- In-text Questions — Ratios in Maps Page 56
- Sections 3.2 Ratios in Maps · 3.3 Ratios with More than 2 Terms — In-text Questions Page 57
- In-text Questions — Ratios with More than 2 Terms Page 58
- Figure it Out — Dividing a Whole in a Given Ratio Page 60
- In-text Questions — A Slice of the Pie Page 61
- Figure it Out — A Slice of the Pie Page 62
- In-text Questions — Inverse Proportions Page 63
- In-text Questions — Inverse Proportions Page 64
- Figure it Out — Inverse Proportions Page 65
- In-text Questions — Inverse Proportions Page 66
- –68Section 3.6 Inverse Proportions — Figure it Out Page 67