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
- Definition: Mixed Fraction
- Structure of Mixed Fractions
- Example 1
- Example 2
- Example 3
- Real-Life Application
- Key Points Summary
CISCE: Class 6
Definition: Mixed Fraction
A fraction that contains a whole number and a proper fraction is called a mixed fraction.
`3 2/3, 4 2/3, 3 7/8` are all examples of mixed fractions.
CISCE: Class 6
Structure of Mixed Fractions
Mixed fractions = `"Quotient" ("Remainder"/"Divisor")`.
CISCE: Class 6
Example 1
`5/2` = `1/2` + `1/2` + `1/2` + `1/2` + `1/2`
= 2 + `1/2`
CISCE: Class 6
Example 2
3 + `3/4`
Solution
- This means 1 + 1 + 1 +`3/4`.
- 1 = `1/4` +`1/4`+ `1/4` +`1/4`.
- (`1/4` +`1/4`+ `1/4` +`1/4`) + ( `1/4` +`1/4`+ `1/4` +`1/4`) + (`1/4` +`1/4`+ `1/4` +`1/4`) + (`1/4` +`1/4`+ `1/4`) = `15/4`
Therefore, (4 × `1/4`) + (4 × `1/4`) + (4 × `1/4`) + (3 × `1/4`) = `15/4`
CISCE: Class 6
Example 3
1 `1/2`
- 1 is the integer part, and `1/2` is the fractional part.
- If half of each of the three circles is colored, the total colored portion is
`1/2`+`1/2`+`1/2`
= `3/2` or 1 `1/2`
CISCE: Class 6
Real-Life Application
You baked cookies:
You have 7 halves of a cookie (`7/2` cookies).
How many whole cookies and how many halves?
-
7 ÷ 2 = 3 (whole cookies), remainder 1
-
That’s 3`1/2` cookies.
CISCE: Class 6
Key Points Summary
-
A mixed fraction = a whole number + part (fraction) of a whole.
-
Improper fractions can be easily written as mixed fractions by dividing.
-
Mixed fractions are handy in daily life: cooking, measuring, and sharing.
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Series: Concept of Improper Fraction and Mixed Fraction
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