Topics
Integers
- Natural Numbers
- Whole Numbers
- Negative and Positive Numbers
- Integers
- Representation of Integers on the Number Line
- Ordering of Integers
- Addition of Integers
- Subtraction of Integers
- Properties of Addition and Subtraction of Integers
- Multiplication of a Positive and a Negative Integers
- Multiplication of Two Negative Integers
- Product of Three Or More Negative Integers
- Closure Property of Multiplication of Integers
- Commutative Property of Multiplication of Integers
- Multiplication of Integers with Zero
- Multiplicative Identity of Integers
- Associative Property of Multiplication of Integers
- Distributive Property of Multiplication of Integers
- Making Multiplication Easier of Integers
- Division of Integers
- Properties of Division of Integers
Fractions and Decimals
- Concept of Fraction
- Types of Fractions
- Concept of Proper and Improper Fractions
- Concept of Mixed Fractions
- Concept of Equivalent Fractions
- Like and Unlike Fraction
- Comparing Fractions
- Addition of Fraction
- Subtraction of Fraction
- Multiplication of a Fraction by a Whole Number
- Using Operator 'Of' with Multiplication and Division
- Multiplication of Fraction
- Division of Fractions
- Concept of Reciprocals or Multiplicative Inverses
- Problems Based on Fraction
- The Decimal Number System
- Comparing Decimal Numbers
- Addition of Decimal Fraction
- Subtraction of Decimal Numbers
- Multiplication of Decimal Numbers
- Division of Decimal Numbers
- Problems Based on Decimal Numbers
Data Handling
Simple Equations
Lines and Angles
The Triangle and Its Properties
- Basic Concepts of Triangles
- Classification of Triangles based on Sides
- Classification of Triangles based on Angles
- Median of a Triangle
- Altitudes of a Triangle
- Exterior Angle of a Triangle and Its Property
- Some Special Types of Triangles - Equilateral and Isosceles Triangles
- Basic Properties of a Triangle
- Right-angled Triangles and Pythagoras Property
Comparing Quantities
- Ratio
- Concept of Equivalent Ratios
- Proportion
- Unitary Method
- Basic Concept of Percentage
- Estimation in Percentages
- Interpreting Percentages
- Conversion between Percentage and Fraction or Decimal
- Ratios to Percents
- Increase Or Decrease as Percent
- Basic Concepts of Profit and Loss
- Profit or Loss as a Percentage
- Calculation of Interest
Congruence of Triangles
- Similarity and Congruency of Figures
- Congruence Among Line Segments
- Congruence of Angles
- Congruence of Triangles
- Criteria for Congruence of Triangles
- Criteria for Similarity of Triangles
- SAS Congruence Criterion
- ASA Congruence Criterion
- RHS Congruence Criterion
- Exceptional Criteria for Congruence of Triangles
Rational Numbers
- Rational Numbers
- Equivalent Rational Number
- Positive and Negative Rational Numbers
- Rational Numbers on a Number Line
- Rational Numbers in Standard Form
- Comparison of Rational Numbers
- Rational Numbers Between Two Rational Numbers
- Addition of Rational Number
- Subtraction of Rational Number
- Multiplication of Rational Numbers
- Division of Rational Numbers
Perimeter and Area
- Basic Concepts in Mensuration
- Concept of Perimeter
- Perimeter of a Rectangle
- Perimeter of Squares
- Perimeter of Triangle
- Perimeter of Polygon
- Concept of Area
- Area of Square
- Area of Rectangle
- Triangles as Parts of Rectangles and Square
- Generalising for Other Congruent Parts of Rectangles
- Area of a Parallelogram
- Area of a Triangle
- Circumference of a Circle
- Area of Circle
- Conversion of Units
- Problems based on Perimeter
- Problems based on Area
Practical Geometry
- Construction of a Line Parallel to a Given Line, Through a Point Not on the Line
- Construction of Triangles
- Constructing a Triangle When the Length of Its Three Sides Are Known (SSS Criterion)
- Constructing a Triangle When the Lengths of Two Sides and the Measure of the Angle Between Them Are Known. (SAS Criterion)
- Constructing a Triangle When the Measures of Two of Its Angles and the Length of the Side Included Between Them is Given. (ASA Criterion)
- Constructing a Right-angled Triangle When the Length of One Leg and Its Hypotenuse Are Given (RHS Criterion)
Algebraic Expressions
Exponents and Powers
- Concept of Exponents
- Multiplying Powers with the Same Base
- Dividing Powers with the Same Base
- Taking Power of a Power
- Multiplying Powers with Different Base and Same Exponents
- Dividing Powers with Different Base and Same Exponents
- Numbers with Exponent Zero, One, Negative Exponents
- Miscellaneous Examples Using the Laws of Exponents
- Decimal Number System Using Exponents and Powers
- Crores
Symmetry
Visualizing Solid Shapes
- Introduction
- Steps to Add Decimals
- Example 1
- Example 2
- Key Points Summary
CISCE: Class 6
Introduction
-
Decimals are another way to write numbers that are not whole.
-
A decimal point (.) separates the whole part from the fractional part (tenths, hundredths, etc.).
-
We add decimals the same way we add whole numbers—by aligning the decimal points.
CISCE: Class 6
Steps to Add Decimals
CISCE: Class 6
Example 1
Add 0.35 and 0.42.
0.35 + 0.42 = 0.77
| Ones | Tenths | Hundredths | |
| 0 | 3 | 5 | |
| + | 0 | 4 | 2 |
| 0 | 7 | 7 |
CISCE: Class 6
Example 2
Add 0.68 and 0.54
0.68 + 0.54 = 1.22
0.68 + 0.54 = 1.22
| Ones | Tenths | Hundredths | |
| 0 | 6 | 8 | |
| + | 0 | 5 | 4 |
| 1 | 2 | 2 |
Maharashtra State Board: Class 5
Key Points Summary
- Always align decimals before adding.
-
Add like whole numbers, starting from the right.
-
Carry over when the column sum is greater than 9.
-
Keep the decimal point in the same vertical line.
-
Decimals appear in real life in money, length, weight, and measurements.
Example Question 1
Add: 1067.080 and 0000.943
|
|
Thousands |
Hundreds |
Ones |
Tenths |
Hundredths |
Thousandths |
Ten Thousandths |
| 1 | 0 | 6 | 7 | 0 | 8 | 0 | |
| + | 0 | 9 | 4 | 3 | 0 | ||
| 1 | 0 | 6 | 8 | 0 | 2 | 3 |
Example Question 2
Add: 1.5 and 5.006
|
|
Ones |
Tenths |
Hundredths |
Thousandths |
| 1 | 5 | 0 | 0 | |
| + | 5 | 0 | 0 | 6 |
| 6 | 5 | 0 | 6 |
Example Question 3
Rahul bought 4 kg 90 g of apples, 2 kg 60 g of grapes and5 kg 300 g of mangoes. Find the total weight of all the fruits he bought.
Weight of apples = 4 kg 90 g= 4.090 kg
Weight of grapes = 2 kg 60 g = 2.060 kg
Weight of mangoes = 5 kg 300 g = 5.300 kg
Therefore, the total weight of the fruits bought is
| 4.090 kg | |
| + | 2.060 kg |
| + | 5.300 kg |
| 11.450 kg |
The total weight of the fruits bought = 11.450 kg.
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