NCERT Class 8 Mathematics Ganita Prakash Part-I: Chapter 7 — Proportional Reasoning-1
This chapter, "Observing Similarity in Change," from NCERT Class 8 Mathematics Ganita Prakash Part-I, introduces the concept of proportional reasoning through the example of digital images. It explains how resizing images affects their appearance and what makes some images look similar while others appear distorted. By comparing the dimensions (width and height) of various images, students learn that similarity is maintained when both dimensions change by the same multiplicative factor. The chapter highlights that proportional changes in width and height lead to similar images, whereas additive changes or non-proportional multiplicative changes result in distortion. This foundational understanding of proportionality is crucial for developing geometric reasoning and problem-solving skills in mathematics.
Quick info
| Board | CBSE / NCERT |
|---|---|
| Class | Class 8 |
| Subject | Mathematics |
| Book | Ganita Prakash Part-I |
| Chapter | Chapter 7 — Proportional Reasoning-1 |
| Language | English |
| PDF type | NCERT Textbook |
| Session | CBSE 2026 |
| Reading time | 2 minutes |
| Word count | 366 |
Learning outcomes
- Understand the concept of similarity in geometric shapes.
- Identify when changes in dimensions are proportional.
- Differentiate between proportional and non-proportional changes.
- Apply proportional reasoning to real-world examples like image resizing.
Vocabulary
| Word | Meaning |
|---|---|
| Similar | Having the same shape, but not necessarily the same size. |
| Proportional | When two quantities change by the same multiplicative factor. |
| Distorted | Altered or twisted out of shape. |
| Factor | A number by which another number is multiplied or divided. |
| Orientation | The relative physical position or direction of something. |
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Practice questions
- If an image's width is multiplied by 3 and its height is multiplied by 3, will the image look similar to the original? Answer: Yes, because both dimensions changed by the same factor (3).
- Image X has width 10 cm and height 5 cm. Image Y has width 20 cm and height 15 cm. Do images X and Y look similar? Answer: No. The width doubled (10 to 20), but the height did not double (5 to 15, which is a factor of 3).
- What is the difference between proportional and non-proportional changes in dimensions? Answer: Proportional changes involve multiplication by the same factor for all dimensions, maintaining similarity. Non-proportional changes do not follow this rule, leading to distortion.
Frequently asked questions
What makes images A, C, and D look similar in the chapter?
Images A, C, and D look similar because their widths and heights have changed by the same multiplicative factor, meaning the changes are proportional.
Why do images B and E look different or distorted?
Images B and E look distorted because their widths and heights have not changed by the same factor, making the changes non-proportional.
What is the role of factors in determining image similarity?
When resizing an image, if the width and height are multiplied by the same factor, the image remains similar. If the factors are different, the image becomes distorted.
How does subtraction affect image similarity compared to multiplication?
Subtracting the same value from width and height does not guarantee similarity, as seen with image A and B. Similarity is primarily determined by proportional (multiplicative) changes.
What does it mean for changes to be 'proportional' in this context?
It means that the width and height of the image have been multiplied by the same number (factor) to achieve the new size.
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NCERT Class 8 Mathematics — Ganita Prakash Part-I — Chapter 7 — Proportional Reasoning-1. Verified by NCERT Help Editorial Team. Reviewed on 29 Jul 2026. Last updated 10 Aug 2026.