Topics
Number System (Including Estimation and Approximation)
Number System
Theme 1 : Numbers
Number System(Consolidating the Sense of Numberness)
Ratio and Proportion
Theme 2 : Ratio, Proportion and Arithmetic Problems
Numbers in Indian and International Systems (With Comparison)
Estimation
Theme 3 : Algebra
Numbers in India and International System (With Comparison)
Algebra
Natural Numbers and Whole Numbers (Including Number Line and Patterns)
Place Value
Negative Numbers and Integers
Geometry
Theme 4 : Geometry
Mensuration
Theme 5 : Mensuration
Sets
Natural Numbers and Whole Numbers (Including Patterns)
Negative Numbers and Integers
Theme 6 : Statistics
Data Handling
Fractions
Number Line
Decimal Fractions
Playing with Numbers (Including H.C.F. and L.C.M.)
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
Ratio and Proportion (Including Unitary Method)
Sets
Percent (Percentage)
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)
Fundamental Concepts (Including Angles and their Properties)
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
Triangles (Including Types and Properties of Triangles)
Quadrilaterals
Percent (Percentage)
Circles
Idea of Speed, Distance and Time
Symmetry
Fundamental Concepts
Constructions
Fundamental Operations (Related to Algebraic Expressions)
Substitution (Including Use of Brackets as Grouping Symbols)
Recognition of Solids
Framing Algebraic Expressions (Including Evaluation)
Perimeter and Area of Plane Figures
Data Handling (Including Mean and Median)
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
- Introduction
- Converting into Simple Ratio
- Expressing Quantities in the Form a:b:c
- Simplifying the Ratio a : b : c
- Real-Life Application
- Key Points Summary
Introduction
Ratios help compare quantities easily—recipes, sharing, and even map reading use ratios. Simplifying them makes these comparisons clearer.
Converting into Simple Ratio
Example (i): 3`1 / 2`: 2`1 / 3`
Method 1: Divide the first term of the ratio by its second term and then simplify.
Given ratio: 3`1 / 2` : 2`1 / 3` = `7 / 2 ` : `7 / 3`
= `7 / 2 ` × `3 / 7`
= `3 / 2`
= 3 : 2
Method 2: Multiply each term of the ratio by the L.C.M. of their consequents and then simplify.
Given ratio: = `7 / 2 ` : `7 / 3`
=`7 / 2 ` × 6 : `7 / 3` × 6 (LCM of 2 and 3 is 6)
= 21 : 14
= `3 / 2`
= 3 : 2
Expressing Quantities in the Form a:b:c
Example: If the ratio of ages between Geeta, Harry, and John is 6 : 8 : 7 and k = 2.
- The age of Geeta = 6k = 6 × 2 years = 12 years.
- The age of Harry = 8k = 8 × 2 years = 16 years.
- The age of John = 7k = 7 × 2 years = 14 years.
Simplifying the Ratio a : b : c
Example:
1. Simplify the ratios:
`2 / 3` : `1 / 2` : `4 / 5`
Solution:
Since the L.C.M. of consequents (denominators) 3, 2 and 5 is 30
`2 / 3` : `1 / 2` : `4 / 5` = `2 / 3` × 30 : `1 / 2` × 30 : `4 / 5` × 30
= 20 : 15 : 24
2. `1 / 6` : `1 / 3` : `1 / 8`
Since the L.C.M. of consequents (denominators) 6, 3 and 8 is 24
`1 / 6` : `1 / 3` : `1 / 8` = `1 / 6` × 24 : `1 / 3` × 24 : `1 / 8` × 24
= 4 : 8 : 3
Real-Life Application
Recipe Problem:
You need 3 cups of flour and 2 cups of sugar for a recipe.
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The ratio of flour to sugar is 3:2.
Key Points Summary
-
Always write values using the same unit.
-
Convert fractions to whole numbers when you can.
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Simplify by dividing both numbers by their HCF.
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The simplest ratio is when no number divides both parts further.
