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Rational Numbers — Concept Maps

Gujarat Board · Class 8 · Mathematics

3 concept maps of Rational Numbers for Gujarat Board Class 8 Mathematics, each also written out as a text outline.

45 questions4 formulas & key relations5 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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3 Concept Maps

Chapter Overview: Rational Numbers and Their Properties

Chapter Overview: Rational Numbers and Their Properties

The map in words

  • Rational Numbers
    • Definition
      • Form p over q
      • p and q are integers
      • q is not zero
      • Examples
        • Negative 2 over 3
        • 6 over 7
        • Zero
        • Negative 5
    • Number Systems
      • Natural Numbers
      • Whole Numbers
      • Integers
      • Rational Numbers
    • Properties
      • Closure
        • Addition Yes
        • Subtraction Yes
        • Multiplication Yes
        • Division No
      • Commutativity
        • Addition Yes
        • Subtraction No
        • Multiplication Yes
        • Division No
      • Associativity
        • Addition Yes
        • Subtraction No
        • Multiplication Yes
        • Division No
      • Distributivity
        • a times b plus c
        • equals ab plus ac
    • Identity Elements
      • Additive Identity Zero
      • Multiplicative Identity One
    • Key Formulas
      • a plus b equals b plus a
      • a times b plus c equals ab plus ac
      • a plus zero equals a
      • a times one equals a

Rational Numbers: Complete Concept Map

Rational Numbers: Complete Concept Map

The map in words

  • Rational Numbers
    • Definition
      • Form p/q
      • p and q are integers
      • q not equal to zero
      • Examples: 3/4, -5/7, 0
    • Closure Property
      • Under addition
        • a + b always rational
      • Under subtraction
        • a - b always rational
      • Under multiplication
        • a × b always rational
      • Under division
        • Except by zero
    • Commutative Property
      • Addition
        • a + b = b + a
      • Multiplication
        • a × b = b × a
      • Not for subtraction
      • Not for division
    • Associative Property
      • Addition
        • a + b) + c = a + (b + c
      • Multiplication
        • a × b) × c = a × (b × c
      • Not for subtraction
      • Not for division
    • Identity Elements
      • Additive Identity
        • Zero: a + 0 = a
      • Multiplicative Identity
        • One: a × 1 = a
    • Distributive Property
      • Multiplication over addition
        • a(b + c) = ab + ac
      • Multiplication over subtraction
        • a(b - c) = ab - ac
    • Number System Hierarchy
      • Natural numbers
      • Whole numbers
      • Integers
      • Rational numbers

Rational Numbers - Complete Overview

Rational Numbers - Complete Overview

The map in words

  • Rational Numbers
    • Definition
      • Form p divided by q
      • p and q are integers
      • q is not equal to 0
    • Types
      • Positive Rationals
        • Example 3 by 7
        • Example 5 by 8
      • Negative Rationals
        • Example minus 2 by 3
        • Example minus 7 by 9
      • Zero
        • Written as 0 by 1
    • Includes
      • Natural Numbers
      • Whole Numbers
      • Integers
      • All Fractions
    • Properties
      • Closure
        • Add Yes
        • Sub Yes
        • Mul Yes
        • Div No
      • Commutativity
        • Add Yes
        • Sub No
        • Mul Yes
        • Div No
      • Associativity
        • Add Yes
        • Sub No
        • Mul Yes
        • Div No
      • Distributivity
        • Mul over Add Yes
        • Mul over Sub Yes
    • Identities
      • Additive Identity Zero
      • Multiplicative Identity One
    • Inverses
      • Additive Inverse minus a
      • Multiplicative Inverse 1 by a

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Frequently Asked Questions

What are the important topics in Rational Numbers for Gujarat Board Class 8 Mathematics?
Key topics in Rational Numbers include What Are Rational Numbers?, Closure Property, Commutativity Property, Associativity Property. Study these first, then practise questions on each for Class 8 exams.
What do the concept maps for Rational Numbers show?
The 3 maps show how the ideas in Rational Numbers connect: Chapter Overview: Rational Numbers and Their Properties; Rational Numbers: Complete Concept Map. Each map is also written out as an outline on this page.
How should I revise Rational Numbers for Class 8 exams?
Learn the core ideas first, then work through the 45 practice questions on Rational Numbers. Revise 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.

More resources for Rational Numbers

All Gujarat Board Class 8 Mathematics Concept Maps

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