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Rational Numbers

Gujarat Board · Class 8 · Mathematics

Quick revision notes for Rational Numbers — Gujarat Board Class 8 Mathematics. Key concepts, formulas, and definitions for last-minute revision.

45 questions5 concepts

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A nested Venn diagram illustrating the relationships between natural numbers (N), integers (Z), rational numbers (Q), and real numbers (R) as subsets of each other.
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Key Topics to Revise

1

What Are Rational Numbers?

  • A rational number is any number that can be written as p/q where p and q are integers and q ≠ 0.
  • Examples: -2/3, 6/7, 9/-5, 0, -2, 4 are all rational numbers.
  • Every integer is a rational number (e.g., -2 = -2/1).
2

Closure Property

  • A set is CLOSED under an operation if performing that operation on any two numbers from the set always gives a result that is also in the set.
  • Rational numbers are CLOSED under addition: a + b is always a rational number.
  • Rational numbers are CLOSED under subtraction: a - b is always a rational number.
3

Commutativity Property

  • An operation is COMMUTATIVE if changing the order of the two numbers does NOT change the result.
  • Addition is commutative for rational numbers: a + b = b + a.
  • Multiplication is commutative for rational numbers: a × b = b × a.
4

Associativity Property

  • An operation is ASSOCIATIVE if grouping of numbers does NOT change the result: a * (b * c) = (a * b) * c.
  • Addition is associative for rational numbers: a + (b + c) = (a + b) + c.
  • Multiplication is associative for rational numbers: a × (b × c) = (a × b) × c.

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Full Notes

Key Concepts

A rational number is any numberA set of numbers is closedAn operation is commutative if changingAn operation is associative ifZero is the additive identity

Frequently Asked Questions

What are the important topics in Rational Numbers for Gujarat Board Class 8 Mathematics?
Key topics in Rational Numbers include Chapter Overview: Rational Numbers and Their Properties, Rational Numbers: Complete Concept Map, Rational Numbers - Complete Overview. These are the concepts Gujarat Board Class 8 examiners draw on most — study them first, then practise related questions.
How to score full marks in Rational Numbers — Gujarat Board Class 8 Mathematics?
Understand the core concepts first, then work through the 45 practice questions available for this chapter. Revise formulas and definitions regularly, and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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