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Class 7
Rational Numbers
Simplifying Rational Numbers
Class 7
1.
Integers
1.1.
Introduction to Integers
1.2.
Operations on Integers
1.2.1.
Multiplication and Division of Integers
1.2.1.1.
Multiplication of Integers
1.2.1.2.
Properties of Multiplication of Integers
1.2.1.3.
Division of Integers
1.2.1.4.
Properties of Division of Integers
1.2.2.
Use of Brackets
1.2.3.
Word Problems on Integers
2.
Fractions and Decimals
2.1.
Fractions
2.1.1.
Revisiting Basics
2.1.2.
Equivalent Fractions
2.1.3.
Comparing Fractions
2.1.3.1.
Comparing Like Fractions
2.1.3.2.
Comparing Unlike Fractions
2.1.4.
Operations on Fractions
2.1.4.1.
Addition of Fractions
2.1.4.1.1.
Addition of Like Fractions
2.1.4.1.2.
Addition of Unlike Fractions
2.1.4.1.3.
Addition of Mixed Fractions
2.1.4.2.
Subtraction of Fractions
2.1.4.2.1.
Subtraction of Like Fractions
2.1.4.2.2.
Subtraction of Unlike Fractions
2.1.4.2.3.
Subtraction of Mixed Fractions
2.1.4.3.
Addition and Subtraction of Fractions
2.1.4.4.
Multiplication of Fractions
2.1.4.4.1.
Multiplication of Fractions
2.1.4.4.2.
Use of 'OF'
2.1.4.5.
Division of Fractions
2.1.4.5.1.
Reciprocal of a Fraction
2.1.4.5.2.
Division of Fractions
2.1.4.6.
Mixed Operations on fractions
2.1.4.7.
Word Problems on Fractions
2.1.4.7.1.
Word Problems on Addition of Fractions
2.1.4.7.2.
Word Problems on Subtraction of Fractions
2.1.4.7.3.
Word Problems on Addition and Subtraction of Fractions
2.1.4.7.4.
Word Problems on Multiplication of Fractions
2.1.4.7.5.
Word Problems on Division of Fractions
2.2.
Decimals
2.2.1.
Revisiting Basics
2.2.2.
Addition and Subtraction of Decimals
2.2.2.1.
Addition of Decimals
2.2.2.2.
Subtraction of Decimals
2.2.2.3.
Mixed Operations on Decimals: Addition and Subtraction
2.2.2.4.
Word Problems on Addition and Subtraction of Decimals
2.2.3.
Multiplication and Division of Decimals
2.2.3.1.
Multiplication of Decimals
2.2.3.2.
Division of Decimals
2.2.3.3.
Word Problems on Multiplication of Decimals
2.2.3.4.
Word Problems on Division of Decimals
2.2.3.5.
Mixed Operations on Decimals
3.
Data Handling
3.1.
Tabular Representation of Data
3.2.
Mean, Median, and Mode
3.2.1.
Mean
3.2.2.
Median
3.2.3.
Mode
3.3.
Bar Graphs
3.3.1.
Drawing Bar Graphs
3.3.2.
Interpreting Bar Graphs
3.4.
Probability
4.
Linear Equations in One Variable
4.1.
Understanding Linear Equation
4.2.
Writing Statements as Equations and Vice Versa
4.3.
Verify that the Given Solution is the Solution of the Linear Equation
4.4.
Solving Linear Equations
4.5.
Word Problems Based on Linear Equations
5.
Lines and Angles
5.1.
Types of Angles
5.1.1.
Complementary and Supplementary Angles
5.1.2.
Linear Pair of Angles
5.1.3.
Vertically Opposite Angles
5.1.4.
Angles Around a Point
5.2.
Angles Formed when a Transversal Cuts Two Parallel Lines
6.
The Triangle and its Properties
6.1.
Triangles
6.1.1.
Classification of Triangles by the Length of the Sides
6.1.2.
Classification of Triangles by the Angles
6.2.
Properties of a Triangle
6.2.1.
Angle Sum Property of a Triangle
6.2.2.
Exterior Angle Property of a Triangle
6.2.3.
Triangle Inequality
6.2.4.
Pythagoras' Theorem
7.
Congruence of Triangles
7.1.
Understanding the Meaning
7.2.
Congruence of Triangles
8.
Comparing Quantities
8.1.
Introduction
8.2.
Equivalent Ratio
8.3.
Unitary Method
8.3.1.
Problems on Direct Variation
8.3.2.
Problems on Inverse Variation
8.4.
Percentage
8.4.1.
Conversions
8.4.1.1.
Convert a Fraction into Percentage
8.4.1.2.
Convert a Percentage into Fraction
8.4.1.3.
Convert Percentage into a Ratio
8.4.1.4.
Convert a Ratio into Percentage
8.4.1.5.
Convert Percentage into Decimal form
8.4.1.6.
Convert Decimal into Percentage
8.4.2.
Percentage of a Quantity
8.4.3.
Solving Expressions involving Percentages
8.4.4.
Word Problems on Percentage
8.5.
Profit and Loss
8.5.1.
Terms Related to Profit and Loss
8.5.2.
Problems on Finding the Gain/Loss and Gain%/Loss%
8.5.3.
Problems on Finding the SP of the Article
8.5.4.
Problems on Finding the CP of the Article
8.5.5.
Problems on Finding the Number of Articles
8.6.
Simple Interest
8.6.1.
Problems on Calculating the Simple Interest
8.6.2.
Problems on Calculating the Rate Percent
8.6.3.
Problems on Calculating Time Period
8.6.4.
Problems on Calculating the Principal
9.
Rational Numbers
9.1.
Understanding Rational Numbers
9.2.
Equivalent Rational Numbers
9.3.
Comparison of Rational Numbers
9.4.
Representation of Rational Numbers on the Real Line
9.5.
Addition and Subtraction of Rational Numbers
9.5.1.
Addition of Rational Numbers
9.5.2.
Additive Inverse of a Rational Number
9.5.3.
Subtraction of Rational Numbers
9.6.
Multiplication and Division of Rational Numbers
9.6.1.
Multiplication Of Rational Numbers
9.6.2.
Reciprocal of Rational Number
9.6.3.
Division Of Rational Numbers
9.7.
Rational Numbers Lying Between Two Rational Numbers
9.8.
Simplifying Rational Numbers
9.9.
Word Problems on Rational Numbers
10.
Practical Geometry
10.1.
Construction of a Line Parallel to a Given Line
10.2.
Construction of a Triangle
10.2.1.
Constructing a Triangle When its Three Sides are Known
10.2.2.
Constructing a Triangle When Two Sides and Angle Between Them are Known
10.2.3.
Constructing a Triangle When Two Angles and Side Included Between are Known
10.2.4.
Constructing a Right-Angled Triangle When One Leg and Hypotenuse are Known
11.
Perimeter and Area
11.1.
Standard Units of Area
11.2.
Area and Perimeter of a Square
11.3.
Area and Perimeter of a Rectangle
11.4.
Area of 4 Walls of a Room
11.5.
Area between Two Rectangles
11.6.
Area and Perimeter of Triangles
11.7.
Area and Perimeter of Parallelogram and Rhombus
11.8.
Circumference and Area of a Circle
11.9.
Area Enclosed Between Two Different Shapes
12.
Algebraic Expressions
12.1.
Variables and Constants
12.2.
Types of Algebraic Expressions
12.3.
Finding the Value of an Algebraic Expression
12.4.
Operations on Algebraic Expressions
12.4.1.
Addition of Algebraic Expressions
12.4.2.
Subtraction of Algebraic Expressions
12.4.3.
Addition and Subtraction of Algebraic Expressions
12.4.4.
Multiplication of Algebraic Expressions
12.4.4.1.
Multiplication of Monomials
12.4.4.2.
Multiplication of a Monomial and a Binomial
12.4.4.3.
Multiplication of two Binomials
12.5.
Simplifying Algebraic Expression by Eliminating the Grouping Symbols
13.
Exponents and Powers
13.1.
Introduction to Exponents
13.2.
Exponent of a Rational Number
13.3.
Express Rational Numbers in Exponential Form
13.4.
Solving Expressions Involving Exponents
13.5.
Laws of Exponents
13.6.
Word Problems on Exponents
13.7.
Finding the Unknown from the Given Exponential Equation
13.8.
Standard Form of Large Numbers
13.9.
Standard Form of Small Numbers
13.10.
Expanded Form of Large Numbers
14.
Symmetry
14.1.
Linear Symmetry
14.1.1.
Linear Symmetry Around Us
14.1.2.
Linear Symmetry in Geometric Figures
14.1.3.
Linear Symmetry in Alphabets
14.2.
Rotational Symmetry
14.2.1.
Rotational Symmetry in Figures and Alphabets
15.
Visualising Solid Shapes
15.1.
Identifying 3-D Shapes
15.2.
Faces, Edges and Vertices of 3-D Shapes (Cuboid, Cube, Cone, Cylinder, and Sphere)
15.3.
Net of a 3-D Shape
Class 7 NCERT (CBSE and ICSE)
Simplifying Rational Numbers
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