Topics
Number System(Consolidating the Sense of Numberness)
Number System
Estimation
Ratio and Proportion
Algebra
Numbers in India and International System (With Comparison)
Geometry
Place Value
Mensuration
Natural Numbers and Whole Numbers (Including Patterns)
Data Handling
Negative Numbers and Integers
Number Line
HCF and LCM
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
Sets
Ratio
Proportion (Including Word Problems)
Unitary Method
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
Decimal Fractions
Percent (Percentage)
Idea of Speed, Distance and Time
Fundamental Concepts
Fundamental Operations (Related to Algebraic Expressions)
Substitution (Including Use of Brackets as Grouping Symbols)
Framing Algebraic Expressions (Including Evaluation)
Simple (Linear) Equations (Including Word Problems)
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
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.
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.
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`.
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.
