Topics
Number System
Number System (Including Estimation and Approximation)
Number System(Consolidating the Sense of Numberness)
Theme 1 : Numbers
Estimation
Theme 2 : Ratio, Proportion and Arithmetic Problems
Numbers in Indian and International Systems (With Comparison)
Ratio and Proportion
Algebra
Natural Numbers and Whole Numbers (Including Number Line and Patterns)
Numbers in India and International System (With Comparison)
Theme 3 : Algebra
Theme 4 : Geometry
Place Value
Negative Numbers and Integers
Geometry
Mensuration
Theme 5 : Mensuration
Natural Numbers and Whole Numbers (Including Patterns)
Sets
Data Handling
Fractions
Theme 6 : Statistics
Negative Numbers and Integers
Decimal Fractions
Number Line
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
Ratio
Idea of Speed, Distance and Time
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
Triangles (Including Types and Properties of Triangles)
Decimal Fractions
Quadrilaterals
Percent (Percentage)
Circles
Idea of Speed, Distance and Time
Constructions
Symmetry
Fundamental Concepts
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
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
- Steps for Addition of Like Terms
- Examples of Like Terms
- Addition of Unlike Terms
- Real-Life Application
- Key Points Summary
Introduction
-
Addition of Like Terms: Like terms are terms that have the same variables raised to the same powers. The process of adding like terms involves adding the coefficients of the terms.
-
Addition of Unlike Terms: Unlike terms have different variables or powers. They cannot be added to form a single term. However, they can be written together in the form of an expression, with each term separated by a "+" or "-" sign.
Steps for Addition of Like Terms
- Step 1: Identify Like Terms
2x,3x - Step 2: Combine Coefficients
(2 + 3)x - Step 3: Simplify the Result
5x
Examples of Like Terms
Example 1
3x + 5x
= (3 + 5)x
= 8x
Example 2
4y² + (–2y²)
= (4 – 2)y²
= 2y²
Example 3
2ab + 3ab + 5ab
= (2 + 3 + 5) ab
= 10ab
Example 4
-
7x + (–3x) = (7 – 3)x = 4x
-
−3xy², −5xy², and −xy² = (−3 − 5 − 1)xy² = −9xy²
-
(–3m) + (–2m) = (–3 – 2)m = –5m
Addition of Unlike Terms
Unlike Terms – Cannot Be Added
Unlike terms differ in letters or powers. They stay separate with + or – signs.
Examples:
3x + 4y → cannot combine → write as 3x + 4y
2a² + 5a b → write as 2a² + 5ab
2y³, −5xy and 3x³ → write as = 2y³ − 5xy + 3x³
Real-Life Application
Grocery Shopping and Budgeting
- When shopping for fruits, you might buy different quantities of the same item at different times. For example, if you purchase 3 kg of apples today and 5 kg tomorrow, you simply add the like quantities:
3 kg apples + 5 kg apples = 8 kg apples. - However, you wouldn’t combine apples with oranges: 3 kg apples + 2 kg oranges remains 3 kg apples + 2 kg oranges. This mirrors adding like terms (same items) and leaving unlike terms (different items) separate.
Key Points Summary
-
Like terms: Same letters & powers → add coefficients
-
Unlike terms: Different letters or powers → keep separate
-
Sign matters: Treat – as part of the number
