Topics
Number System
Number System (Including Estimation and Approximation)
Number System(Consolidating the Sense of Numberness)
Theme 1 : Numbers
Ratio and Proportion
Numbers in Indian and International Systems (With Comparison)
Theme 2 : Ratio, Proportion and Arithmetic Problems
Estimation
Numbers in India and International System (With Comparison)
Natural Numbers and Whole Numbers (Including Number Line and Patterns)
Theme 3 : Algebra
Algebra
Theme 4 : Geometry
Negative Numbers and Integers
Geometry
Place Value
Sets
Natural Numbers and Whole Numbers (Including Patterns)
Mensuration
Theme 5 : Mensuration
Theme 6 : Statistics
Data Handling
Negative Numbers and Integers
Fractions
Number Line
Decimal Fractions
HCF and LCM
Playing with Numbers (Including H.C.F. and L.C.M.)
Playing with Numbers
- Simplification of Brackets
- Finding Factors Using Rectangular Arrangements and Division
- Factors and Common Factors
- Multiples and Common Multiples
- Concept of Even and Odd Number
- Tests for Divisibility of Numbers
- Divisibility by 2
- Divisibility by 4
- Divisibility by 8
- Divisibility by 3
- Divisibility by 6
- Divisibility by 9
- Divisibility by 5
- Divisibility by 11
Ratio and Proportion (Including Unitary Method)
Percent (Percentage)
Sets
Idea of Speed, Distance and Time
Ratio
Fundamental Concepts (With operations on Algebraic Expressions)
Proportion (Including Word Problems)
Unitary Method
Framing Algebraic Expressions (Including Substitution and Linear Equations)
Fractions
- Concept of Fraction
- Types of Fractions
- Concept of Proper and Improper Fractions
- Concept of Mixed Fractions
- Like and Unlike Fraction
- Concept of Equivalent Fractions
- Conversion between Improper and Mixed fraction
- Conversion between Unlike and Like Fractions
- Simplest Form of a Fractions
- Comparing Fractions
- Addition of Fraction
- Subtraction of Fraction
- Multiplication of Fraction
- Division of Fractions
- Using Operator 'Of' with Multiplication and Division
- BODMAS Rule
- Problems Based on Fraction
Fundamental Concepts (Including Angles and their Properties)
Triangles (Including Types and Properties of Triangles)
Decimal Fractions
Quadrilaterals
Percent (Percentage)
Idea of Speed, Distance and Time
Circles
Fundamental Concepts
Constructions
Symmetry
Fundamental Operations (Related to Algebraic Expressions)
Recognition of Solids
Substitution (Including Use of Brackets as Grouping Symbols)
Framing Algebraic Expressions (Including Evaluation)
Perimeter and Area of Plane Figures
Simple (Linear) Equations (Including Word Problems)
Data Handling (Including Mean and Median)
Fundamental Concepts
Angles (With Their Types)
Properties of Angles and Lines (Including Parallel Lines)
Triangles (Including Types, Properties and Constructions)
Quadrilateral
Polygons
The Circle
Symmetry (Including Constructions on Symmetry)
Recognition of Solids
Perimeter and Area of Plane Figures
Data Handling (Including Pictograph and Bar Graph)
Mean and Median
- Definition: Simplest Form
- Method 1: Divide the Numerator and Denominator by their HCF
- Method 2: Use Prime Factorization to Cancel Common Factors
- Key Points Summary
CISCE: Class 6
Definition: Simplest Form
A fraction is said to be in the simplest (or lowest) form if its numerator and denominator have no common factor except 1.
`4/3, 2/5` etc. are examples of the simplest form of a fraction.
CISCE: Class 6
Method 1: Divide the Numerator and Denominator by their HCF
Step 1: Find the Highest Common Factor (HCF) of the numerator and denominator.
Step 2: Divide both the numerator and denominator by this HCF.
Example:
Consider the fraction `48/60`.
- The H.C.F. of 48 and 60 is 12.
- Divide both the numerator and denominator by 12.
Thus, `48/60` = `"48 ÷ 12"/"60 ÷ 12"` = `4/5` - `4/5` is the fraction in its lowest terms.
CISCE: Class 6
Method 2: Use Prime Factorization to Cancel Common Factors
Step 1: Express the numerator and denominator as products of prime factors.
Step 2: Cancel common factors.
Example:
`48/60` = `(\cancel(2) xx \cancel(2) xx 2 xx 2 xx \cancel(3))/(\cancel(2) xx \cancel(2) xx \cancel(3) xx 5)` = `"2 × 2"/"5"` = `4/5`.
CISCE: Class 6
Key Points Summary
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Simplest form: The only common factor between the numerator and denominator is 1.
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Use HCF to simplify faster.
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Simpler fractions make calculations easier.
Test Yourself
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