NCERT Solutions for Ganita Prakash (Part 1) Chapter 7 Proportional Reasoning-1
Updated on 2026-09-05
About this chapter
Two figures look alike when their measurements change by the same factor (multiplication). Changing both by the same amount (subtraction) distorts them — that is exactly why image B, made by taking 20 mm off both sides of A, looks elongated. A ratio a : b says that for every a units of the first quantity there are b units of the second. Dividing both terms by their HCF puts the ratio in its simplest form, which is the fingerprint used to compare ratios. Two ratios are in proportion, written a : b :: c : d, when their simplest forms agree. Algebraically this is the same as ad = bc — the cross multiplication rule, which the chapter derives rather than states. Trairasika, the Rule of Three: given three of the four terms, the fourth is d = bc⁄a. Āryabhaṭa put it as ichchhāphala = (phala × ichc
- –1607.1 Observing Similarity in Change
- .2 Ratios · 7.3 Ratios in their Simplest Form
- –1677.4 Problem Solving with Proportional Reasoning
- –170Trairasika
- –171Trairasika
- –172Trairasika
- –1747.5 Sharing, but Not Equally! · Activity 3
- .5 Sharing, but Not Equally!
- –1777.6 Unit Conversions (chapter-end set)
Exercises
- –1607.1 Observing Similarity in Change — In-text Questions Page 159
- .2 Ratios · 7.3 Ratios in their Simplest Form — In-text Questions Page 1617
- –1637.4 Problem Solving with Proportional Reasoning (Examples 1–5) — In-text Questions Page 162
- –1657.4 Problem Solving with Proportional Reasoning (Examples 6–7) · Filter Coffee! — In-text Questions Page 164
- –1677.4 Problem Solving with Proportional Reasoning — Figure it Out Page 165
- –170Trairasika — In-text Questions Page 167
- –171Trairasika — Figure it Out Page 170
- –172Trairasika — In-text Questions Page 171
- –1747.5 Sharing, but Not Equally! · Activity 3 — In-text Questions Page 172
- .5 Sharing, but Not Equally! — Figure it Out Page 1757
- –1777.6 Unit Conversions (chapter-end set) — Figure it Out Page 176
- Puzzle Time