Questions from Class 8 Mathematics Chapter 3 Proportional Reasoning-2 come up often in the CBSE Class 8 exam. These class 8 maths handwritten notes chapter 3 Proportional Reasoning-2 follow the 2026-27 NCERT and cover checking if two ratios are proportional, ratios in maps and representative fraction, ratios with more than two terms. This page hosts the notes PDF,.
- CBSE Class 8 Weightage: a scoring chapter in the Mathematics paper, asked in short and long answers.
- What the notes cover: checking if two ratios are proportional, ratios in maps and representative fraction, ratios with more than two terms, dividing a whole in a given ratio.
- Best for: quick revision before Class 8 exams and a strong base for Class 9.
You can read the complete class 8 maths handwritten notes for Proportional Reasoning-2, with key terms, boxed definitions, and quick revision points, in the PDF below.
These handwritten notes are written by subject teachers, mapped to the 2026-27 NCERT, and checked against the last five years of CBSE Class 8 Mathematics papers.
What the Proportional Reasoning-2 Handwritten Notes Cover
This chapter builds on ratios and proportions. You will read map scales, work with ratios that have more than two terms, share a whole in a given ratio, draw pie charts, and tell apart direct and inverse proportion.
- Checking if two ratios are proportional
- Ratios in maps and representative fraction
- Ratios with more than two terms
- Dividing a whole in a given ratio
- Drawing and reading pie charts
- Direct proportion
- Inverse proportion
- Speed, time and work problems
Proportional Reasoning-2 Topic-wise Weightage for CBSE Class 8 Mathematics
Some parts of this chapter are asked more often than others. The table below shows which sub-topics to revise first, based on recent CBSE Class 8 question trends.
| Sub-topic | Weightage | CBSE Frequency |
|---|---|---|
| Dividing a whole in a given ratio | High | asked often |
| Inverse proportion problems | High | asked often |
| Direct proportion problems | High | asked often |
| Drawing and reading pie charts | Medium | asked sometimes |
| Ratios with more than two terms | Medium | asked sometimes |
| Map scale and representative fraction | Low | asked rarely |
Key Terms and Ideas in Proportional Reasoning-2
These are the terms and ideas the exam asks about most. Learn each one so you can define it and use it in your answers.
| Term / Idea | What it means |
|---|---|
| Proportional ratios | a : b and c : d are proportional if a times d equals b times c |
| Representative fraction | a map ratio like 1 : 60,00,000 comparing map distance to real distance |
| Ratio with many terms | a : b : c keeps all parts changing by the same factor |
| Dividing in a ratio | each part is the whole times its share over the sum of shares |
| Pie chart | a circle where each slice angle is proportional to its share of the total |
| Direct proportion | two quantities whose ratio stays the same, so their quotient is constant |
| Inverse proportion | two quantities whose product stays constant, x times y equals k |
| Rule of three | using three known values of a proportion to find the fourth |
How Collegedunia's Handwritten Notes Help You Revise Proportional Reasoning-2
These notes are made for the night before the exam. They keep the facts short and easy to scan. Collegedunia maps every point to the 2026-27 NCERT.
- Clear handwriting: each topic is written in neat, easy-to-read handwriting.
- Boxed key terms: the main terms and definitions are boxed by hand for fast recall.
- Diagrams and tables: simple hand-drawn tables and charts make ideas clear.
- Colour-coded headings: new sub-topics stand out, so you find any section in seconds.
Proportional Reasoning-2 Self-Assessment Quiz
Try these quick questions after you read the notes. Tap each question to check your answer. They cover the points CBSE asks most often.
Are the ratios 6 : 3 and 4 : 2 proportional?
(a) yes (b) no (c) cannot tell (d) only sometimes
Answer: (a) yes - both cross products equal 12
Share 20 in the ratio 2 : 3 : 5. The largest part is?
(a) 4 (b) 6 (c) 10 (d) 12
Answer: (c) 10 - five parts of the ten equal parts
If 5 workers move 4500 bricks, how many move 18000 in a day?
(a) 10 (b) 15 (c) 20 (d) 25
Answer: (c) 20 - direct proportion, four times the bricks
Which pair is in inverse proportion?
(a) speed and time for a fixed distance (b) cloth length and price (c) taps and total water (d) pages and reading time
Answer: (a) speed and time for a fixed distance - their product is the distance
A pie chart slice for 6 of 20 students has what angle?
(a) 90 degrees (b) 108 degrees (c) 120 degrees (d) 60 degrees
Answer: (b) 108 degrees - 6 over 20 times 360
How to Use These Handwritten Notes for Class 8 Mathematics Revision
Use these class 8 maths handwritten notes in two passes. Read them slowly once for the full chapter. Then, near the exam, read only the boxes and key terms for a fast recall.
- Read the notes once with the NCERT chapter open beside you.
- Say each key term and idea in your own words.
- Practise one long-answer question from a past paper.
- On the last day, revise only the key terms and the boxes.
Class 8 Mathematics Handwritten Notes for All Chapters
The table below links the class 8 maths handwritten notes for every chapter. Use it to jump to any other chapter's notes.
| Chapter | Resource |
|---|---|
| Chapter 1 | Fractions in Disguise Handwritten Notes |
| Chapter 2 | The Baudhayana-Pythagoras Theorem Handwritten Notes |
| Chapter 3 | Proportional Reasoning-2 Handwritten Notes |
| Chapter 4 | Exploring Some Geometric Themes Handwritten Notes |
| Chapter 5 | Tales by Dots and Lines Handwritten Notes |
| Chapter 6 | Algebra Play Handwritten Notes |
| Chapter 7 | Area Handwritten Notes |
Proportional Reasoning-2 Class 8 Mathematics Handwritten Notes FAQs
Ques. Where can I download Proportional Reasoning-2 Class 8 Mathematics Handwritten Notes PDF?
Ans. You can download the Proportional Reasoning-2 Class 8 Mathematics Handwritten Notes PDF directly from this page. Both the Normal and HD versions are free.
Ques. Are these handwritten notes aligned with the 2026-27 NCERT?
Ans. Yes. These notes follow the current 2026-27 syllabus for Class 8 Mathematics. the difference between direct and inverse proportion
Ques. How many pages is the Class 8 Mathematics Proportional Reasoning-2 Handwritten Notes PDF?
Ans. The notes run about 20 pages. They cover the full chapter with key terms, hand-drawn boxes, and a short self-assessment quiz.
Ques. What is the main idea of the 8th standard Mathematics chapter Proportional Reasoning-2?
Ans. The main idea is proportional reasoning, where you compare quantities that change together. When they rise and fall together by the same factor it is direct proportion, and when one rises as the other falls it is inverse proportion.
Ques. Are these Proportional Reasoning-2 notes enough for the CBSE Class 8 exam?
Ans. Yes, for revision. The Collegedunia handwritten notes cover every key point and exam term. Read them with the NCERT chapter and practise past questions.
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