Download Proportional Reasoning-1 – NCERT Class 8 Maths Chapter 7 PDF from the new NCERT Class 8 Maths book Ganita Prakash (2026-27). Read the chapter online or download the free PDF. 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.
Proportional Reasoning-1 PDF – Chapter 7 of Ganita Prakash (Part I)
Read the chapter online or download the PDF.
| Chapter | Download | |
|---|---|---|
| Chapter 7 PDF | Proportional Reasoning-1 | View PDF |
| Full book | NCERT Class 8 Maths – Ganita Prakash | View Book |
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What Is in Proportional Reasoning-1? (Class 8 Maths Chapter 7)
- 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 × ichchhā) ÷ pramāṇa.
- To divide a quantity x in the ratio m : n, cut x into m + n equal groups; the two parts are m × x⁄(m+n) and n × x⁄(m+n).
- Not every problem with four numbers is a proportion. When speed rises the time for a fixed journey falls, so 50 : 2 :: 75 : __ is the wrong model. And terms can only be compared after the units are made to match — 4 hours must become 240 minutes, 1 kg must become 1000 g.
Quick revision – Proportional Reasoning-1
| Idea | In symbols | From this chapter | Watch out for |
|---|---|---|---|
| Ratio | A : b | Image A, width : height = 60 : 40 | Order matters — 60 : 40 is not the same as 40 : 60 |
| Terms of a ratio | A and b | 60 and 40 are the terms | Both terms must be in the same unit before you compare |
| Simplest form | Divide both terms by their HCF | 60 : 40 → 3 : 2 (HCF = 20) | Any common factor helps, but only the HCF finishes the job |
| Proportion | A : b :: c : d | 60 : 40 :: 30 : 20 :: 90 : 60 | Same multiplying factor, not the same difference |
| Cross multiplication | Ad = bc | 150 : 90 :: 240 : x ⇒ 150x = 240 × 90 | Each ratio must compare the same two quantities, in the same order |
| Rule of Three (Trairasika) | D = bc⁄a | 120 : 15 :: 80 : 10 (kg of rice) | Only for quantities that rise and fall together |
| Sharing x in the ratio m : n | M × x⁄(m+n) and n × x⁄(m+n) | ₹4,000 in 3 : 1 → ₹3,000 and ₹1,000 | The whole is m + n groups — not m groups, not n |
| Similar figures | Every length × the same factor | Images A, C, D are all 3 : 2 | Adding or subtracting the same length changes the shape |
| Inverse situation | Speed × time = distance (fixed) | 50 km/h for 2 h ⇒ 75 km/h for 1 h 20 min | More speed means less time — the Rule of Three fails here |
| Unit conversion | Match the units first | 1 acre = 43,560 sq ft; 1 L = 1000 mL; 1 m = 3.281 ft | 4 hours = 240 minutes before pairing it with 150 minutes |
Old NCERT vs New – Class 8 Maths
This chapter is from Ganita Prakash, the new NCERT Class 8 Maths book (NCF-SE 2023, used from 2025-26). It replaced the old book “Mathematics”, so chapter numbers and names differ from older PDFs.
Solutions and All Chapters
Answers to the exercises and the full chapter list of Ganita Prakash:
Proportional Reasoning-1 – Overview
| Class | Class 8 |
| Subject | Maths |
| Book | Ganita Prakash – new NCERT book |
| Part | Part I |
| Chapter | 7 of 14 – Proportional Reasoning-1 |
| Book pages | 159 – 177 |
| Edition | NCERT Reprint 2026-27 |
| Session | 2026-27 |
| Free – read online or download |
Class 8 Maths Chapter 7 – FAQs
Where can I download Proportional Reasoning-1 Class 8 PDF?
From the download table on this page – the chapter PDF is free, and the full book is linked too.
What is Class 8 Maths Chapter 7 about?
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.
Is Proportional Reasoning-1 from the new NCERT Class 8 Maths book?
Yes. It is chapter 7 of ganita prakash (part i), the new NCERT Class 8 Maths book for 2026-27.
Is this the latest NCERT edition for 2026-27?
Yes – the PDF is NCERT’s latest edition for the 2026-27 session.
Where are the NCERT Solutions for Class 8 Maths Chapter 7?
Open the NCERT Solutions link above for answers to the exercise questions.