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
- Key Points for Solving Decimal Word Problems
- Example 1
- Example 2
- Example 3
- Key Points Summary
Introduction
Decimals are numbers that have a dot (.) to separate whole numbers from fractional parts, like 2.5 or 15.75.
In real life, we use decimals when we:
-
Talk about money (₹37.80)
-
Measure lengths (2.4 m)
-
Weigh things (2.55 kg)
We multiply decimals to find a total value, and we divide decimals to split something into equal parts.
Key Points for Solving Decimal Word Problems
Example 1
The cost of one metre of cloth is ₹15.75. Find the cost of 2.4 m of cloth.
Solution:
Since cost of 1 m cloth = ₹15.75
Therefore, the cost of 2.4 m cloth = ₹15.75 × 2.4 = ₹37.80.
Example 2
The length of a rod is 28.14 m. If it is divided into 3 equal pieces, find the length of each piece.
Solution:
Clearly, the length of 3 pieces = 28.14 m [The length of the rod = the sum of the lengths of 3 pieces].
and the length of each piece = `28.14/3` m = 9.38 m
Example 3
The total weight of 8 identical bricks is 20.4 kg.
Find :(i) the weight of each brick. (ii) the total weight of 5 bricks.
Solution:
(i) Given weight of 8 bricks = 20.4 kg,
∴ Weight of each brick = `20.4 /8` kg = 2.55 kg
(ii) Since weight of 1 brick = 2.55 kg,
∴ Total weight of 5 bricks = 2.55 kg × 5 = 12.75 kg
Key Points Summary
- Multiply when finding the total from one unit.
- Divide when sharing or splitting equally.
- Always include units in your answer.
- Be careful where you put the decimal point.
