Topics
Number System (Including Estimation and Approximation)
Theme 1 : Numbers
Number System(Consolidating the Sense of Numberness)
Number System
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
Place Value
Geometry
Natural Numbers and Whole Numbers (Including Patterns)
Mensuration
Theme 5 : Mensuration
Sets
Theme 6 : Statistics
Fractions
Negative Numbers and Integers
Data Handling
Decimal Fractions
Number Line
HCF and LCM
Playing with Numbers (Including H.C.F. and L.C.M.)
Ratio and Proportion (Including Unitary Method)
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
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
- Introduction
- Order of Operations
- Example 1
- Example 2
- Real-Life Application
- Key Points Summary
Introduction
When solving a math expression with many operations, you must follow one fixed order so that everyone gets the same answer. This order is known as the BODMAS Rule, and it is applied in all mathematics, from simple school problems to advanced calculations.
Order of Operations
-
Brackets – Solve inside brackets first.
-
Of – Find ‘of’ values (fraction of, powers).
-
Division – From left to right.
-
Multiplication – From left to right.
-
Addition – From left to right.
-
Subtraction – From left to right.
Example 1
`1/3` +`7/9` ÷ ( `7/10` × 1 `1/4`)
= `1/3` + `7/9` ÷ (`7/10` × `5/4`)
= [`7/10` × `5/4` = `7×5/10×4` = `7/8`]
= `1/3` + `7/9` ÷ `7/8`
= `1/3` + `7/9` × `8/7`
= `1/3` + `8/9`
= `3 + 8/9`
= `11/9`
= 1`2/9`
Example 2
Simplify: ( `2/3` + `5/9`) of `9/22` ÷ `2/3` × `4/5` - `1/5`
Solution :
= `11/9` of `9/22` ÷ `2/3` × `4/5` - `1/5`
[Removing 'bracket', we get: ( `2/3` + `5/9` = `6 +5 /9` = `11/9` )
= `1/2` ÷ `2/3` × `4/5` - `1/5`
[ On operating 'of', we get: `11/9` of `9/22` = `11/9` × `9/22` = `1/2`]
= `1/2` × `3/2` × `4/5` − `1/5`
= `"1 × 3 × 4" /"2 × 2 × 5"` − `1/5`
= `3/5` − `1/5`
= `2/5`
Real-Life Application
Imagine sharing chocolates:
-
First, decide the groups (brackets).
-
Give half to each (of).
-
Share equally (division).
-
Hand out several at once (multiplication).
-
Count the total given (addition).
-
Deduct eaten ones (subtraction).
Key Points Summary
-
Follow BODMAS to solve multi-operation problems correctly.
-
Always start with brackets.
-
Do division/multiplication before addition/subtraction.
-
“Of” means multiplication.
Example Question 1
Solve: 2 × {25 × [(113 - 9) + (4 ÷ 2 × 13)]}
2 × {25 × [(113 - 9) + (4 ÷ 2 × 13)]}
= 2 × {25 × [104 + (4 ÷ 2 × 13)]}
= 2 × {25 × [104 + (2 × 13)]}
= 2 × {25 × [104 + 26]}
= 2 × {25 × 130}
= 2 × 3250
= 6500.
