Multiplication Identities ഗുണനസമവാക്യങ്ങൾ
How a rectangle cut into pieces explains (x + y)(u + v), how the same idea turns 26 × 17 into a mental sum, and how algebra proves calendar tricks, digit-reversal puzzles and multiplication-table patterns. An interactive, animated self-study guide: the basics from earlier classes, every idea of the chapter with real-life uses, animated solutions to every textbook question, a revision sheet, and a model test with a fully solved paper.
How to use this guide
🎬 Watch the animations
Every idea has a step-by-step animation. Press Next ▶ to move one step at a time, or ▶▶ Auto play to watch it like a video. You can go back any time.
🖐️ Play with the numbers
Sliders change the numbers in every picture. Seeing the four pieces of a rectangle change together is the fastest way to feel why an identity is true.
✍️ Try before you see
Questions come with a Show answer button. Always attempt the question in your notebook first, then check. The quizzes give instant feedback.
📖 Textbook links
Purple മലയാളം words are the exact terms used in your textbook, so you can match every page here with the book (pages 61–82).
Learning path
Follow the pages in order. If you are comfortable with the distributive law, letters in algebra and the Class 8 identities, you may skim pages 1–4, but do try their quizzes.
The chapter in one picture
Change the four numbers. The big rectangle is (x + y) wide and (u + v) tall, so its area is the product of the two sums. Cutting it along the dotted lines gives four smaller rectangles whose areas are the four products. That one picture is the whole chapter: everything else is this idea used cleverly.
Quick glossary (Malayalam ↔ English)
| Textbook term | English | Meaning |
|---|---|---|
| ഗുണനസമവാക്യം | Multiplication identity | A rule for a product that is true for every choice of numbers |
| സർവസമവാക്യം | Identity | An equation that holds for ALL values of the letters |
| തുക / വ്യത്യാസം | Sum / difference | x + y / x − y |
| ഗുണനഫലം | Product | The result of multiplying |
| പരപ്പളവ് / ചുറ്റളവ് | Area / perimeter | length × breadth / 2(length + breadth) |
| എണ്ണൽസംഖ്യ | Natural number | 1, 2, 3, … |
| ഒറ്റസംഖ്യ / ഇരട്ടസംഖ്യ | Odd / even number | 2n + 1 / 2n |
| അടുത്തടുത്ത സംഖ്യകൾ | Consecutive numbers | x, x + 1, x + 2, … |
| ശിഷ്ടം (മിച്ചം) | Remainder | What is left after division, e.g. 3n + 1 leaves 1 on ÷ 3 |
| രണ്ടക്കസംഖ്യ | Two-digit number | 10m + n with digits m and n |
| ഗുണിതപ്പട്ടിക | Multiplication table | Row m, column n holds mn |
| ക്രിയാകൗതുകങ്ങൾ | Curiosities of operations | Number tricks explained by algebra |
Made for self-learning. Works offline – every page is a single file. Study material prepared by Claude for Madhu's family study folder, October 2026.