Real Numbers രേഖീയസംഖ്യകൾ
Fractions, negatives, √2 and π – every number you have met so far lives on one straight line. This chapter puts them all there, turns “bigger” into “further right”, and introduces the absolute value |x|: the distance of a number from 0. With it you can measure the distance between any two numbers, solve equations like |x − 1| = 3, and find the point exactly halfway. An interactive, animated self-study guide: the basics from earlier classes, every idea of the chapter with real-life examples, 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
Points slide along the number line and distances stretch between them, step by step. Press Next ▶ or ▶▶ Auto play.
🖐️ Play with the numbers
Sliders move points; watch |x|, distances and midpoints update on the line and in the equations together.
✍️ Try before you see
Questions have a Show a hint button and a hidden final answer. Try first in your notebook.
📖 Textbook links
Purple മലയാളം words are the exact terms of your textbook (pages 165–176).
Learning path
Follow the pages in order. If you remember negative numbers and the number line well, you may skim pages 1–4, but do try their quizzes.
The chapter in one picture
Move the two points. The distance between them is always the bigger minus the smaller, |x − y|, and the point halfway is ½(x + y). Rational numbers and irrational ones like √2 and π sit on the same line.
Quick glossary (Malayalam ↔ English)
| Textbook term | English | Meaning |
|---|---|---|
| രേഖീയസംഖ്യകൾ | Real numbers | All numbers that name points on the number line |
| ഭിന്നകസംഖ്യകൾ | Rational numbers | Can be written x/y with integers x, y: 5, −¾, 0, 2.5 |
| അഭിന്നകസംഖ്യകൾ | Irrational numbers | Cannot be written as fractions: √2, √3, π |
| പൂർണ്ണസംഖ്യകൾ | Integers | …, −2, −1, 0, 1, 2, … |
| സംഖ്യാരേഖ | Number line | A line whose points are named by their distance from 0 |
| കേവലമൂല്യം | Absolute value | |x|, the distance of x from 0 |
| അകലം | Distance | Between x and y: |x − y| |
| സ്ഥാനമാറ്റം | Change of position | From x to y: y − x |
| മധ്യബിന്ദു | Midpoint | Halfway point ½(x + y) |
| ഏകകം | Unit (of length) | The length called 1 |
| സംഖ്യാസാന്ദ്രത | Density of numbers | Infinitely many numbers between any two |
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.