Chapter 2 of 25
Concept Maps
Rational Numbers — Concept Maps
ICSE · Class 7 · Mathematics
4 concept maps of Rational Numbers for ICSE Class 7 Mathematics, each also written out as a text outline. Part of the ICSE Class 7 Mathematics syllabus.
39 questions28 flashcards6 formulas & key relations5 concepts
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4 Concept Maps
Rational Numbers – Complete Chapter Overview
The map in words
- Rational Numbers
- Definition
- Form p over q
- p and q are integers
- q is not zero
- Standard Form
- q is positive
- HCF of p and q is 1
- Types
- Positive Rational
- Both signs same
- Examples 3 over 4 and -5 over -7
- Negative Rational
- Opposite signs
- Examples -3 over 4 and 5 over -7
- Zero
- Neither positive nor negative
- Positive Rational
- Number System
- Natural Numbers
- Whole Numbers
- Integers
- Rational Numbers
- Number Line
- Positive numbers on right
- Negative numbers on left
- Denominator divides unit into equal parts
- Comparing
- Positive greater than Negative
- LCM Method
- Cross Multiplication Method
- Ascending Order
- Descending Order
- Numbers Between Two Rationals
- Infinitely many exist
- LCM Method to find them
- Operations
- Addition
- Same Denominator add numerators
- Different Denominator use LCM
- Subtraction
- Add additive inverse
- Same as addition
- Multiplication
- Multiply numerators
- Multiply denominators
- Cancel before multiplying
- Division
- Multiply by reciprocal
- Flip second fraction
- Addition
- Reciprocal
- Flip p over q to get q over p
- Product with original equals 1
- Used in division
- Definition
Rational Numbers Concept Map
The map in words
- Rational Numbers
- Definition
- Form p/q
- p and q integers
- q not equal to 0
- Classification
- Positive Rationals
- Same sign numerator and denominator
- Negative Rationals
- Opposite sign
- Zero
- Neither positive nor negative
- Positive Rationals
- Standard Form
- Positive denominator
- Coprime p and q
- No common factors
- Representation
- Number Line
- Divide units into parts
- Mark positions
- Comparison
- Using signs
- Same denominator
- Cross multiplication
- Number Line
- Operations
- Addition and Subtraction
- Equal denominators
- Unequal denominators with LCM
- Multiplication
- Multiply numerators and denominators
- Simplify by canceling
- Division
- Multiply by reciprocal
- Multiplicative inverse
- Addition and Subtraction
- Properties
- Density
- Infinite numbers between two rationals
- Closure
- All operations produce rationals
- Ordering
- Complete ordering possible
- Density
- Definition
Decision Tree for Rational Number Operations
The map in words
- Start: Choose Operation
- Which Operation?
- Addition/Subtraction: Denominators Equal?
- Yes: Add/Subtract numerators Keep denominator Simplify
- Result
- No: Find L.C.M. of denominators Convert to common denominator Add/Subtract numerators Simplify
- Yes: Add/Subtract numerators Keep denominator Simplify
- Multiplication: Multiply numerators Multiply denominators Simplify
- Division: Find reciprocal of divisor Multiply by reciprocal Simplify
- Comparison: Same Denominator?
- Yes: Compare numerators Larger numerator = Larger fraction
- No: Both Positive or Both Negative?
- Same Sign: Use L.C.M. method to compare
- Opposite Signs: Positive > Negative
- Addition/Subtraction: Denominators Equal?
- Which Operation?
Rational Numbers and their properties, representation, comparison, and operations
The map in words
- Rational Numbers and their properties, representation, comparison, and operations
- Definition of Rational Number
- Standard Form
- Types of Rational Numbers
- Number Line Representation
- Comparing Rational Numbers
- Rational Numbers Between Two Numbers
- Addition of Rational Numbers
- Subtraction of Rational Numbers
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Explore DiagramsFrequently Asked Questions
What are the important topics in Rational Numbers for ICSE Class 7 Mathematics?
Key topics in Rational Numbers include What Rational Numbers Are, Number Line Representation and Comparison, Finding Rational Numbers Between Two Given Numbers, Addition and Subtraction of Rational Numbers. Study these first, then practise questions on each for Class 7 exams.
What do the concept maps for Rational Numbers show?
The 4 maps show how the ideas in Rational Numbers connect: Rational Numbers – Complete Chapter Overview; Rational Numbers Concept Map. Each map is also written out as an outline on this page.
How should I revise Rational Numbers for Class 7 exams?
Learn the core ideas first, then work through the 39 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
Practice Quiz
Test yourself with a quick quiz
Important Questions
Exam-style questions with answers
Revision Notes
Key points for last-minute revision
Formula Sheet
The chapter's formulas in one place
Chapter Summary
Understand the chapter at a glance
Study Plan
Step-by-step plan for this chapter
Flashcards
Quick-fire cards for active recall
Syllabus
What topics to cover
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