Topics
Part 1
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
Large Numbers Around Us
Part 2
Arithmetic Expressions
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
A Peek Beyond the Point
Data Handling
Expressions using Letter-Numbers
Simple Equations
Parallel and Intersecting Lines
Lines and Angles
Number Play
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
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
A Tale of Three Intersecting Lines
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
Working with Fractions
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
Geometric Twins
Algebraic Expressions
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)
Operations with Integers
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
Finding Common Ground
Another Peek Beyond the Point
Symmetry
Visualizing Solid Shapes
Connecting the Dots
Constructions and Tilings
Finding the Unknown
Estimated time: 11 minutes
- Introduction
- Symbol of Percentage
- Formula: Percentage
- Steps to Convert Fractions to Percentages
- Example 1
- Example 2
- Real-Life Examples
- Key Points Summary
CISCE: Class 6
Introduction
What is a Percentage?
- The word "percent" means "out of 100".
-
It tells us how many parts out of 100 something represents.
-
For example, 25% means 25 parts out of 100 parts.
- When a fraction is written in such a way that the denominator is 100, then the numerator of that fraction is called a 'percent' or 'percentage'.
CISCE: Class 6
Symbol of Percentage
-
The symbol for percent is %.
-
So, 75% means 75 out of 100.
CISCE: Class 6
Formula: Percentage
Percentage = `"value"/"Total value"` × 100
% (Percentage) = `"Part"/"Whole"` × 100
Percent is the numerator of a fraction with a denominator of 100.
CISCE: Class 6
Steps to Convert Fractions to Percentages
-
Step 1: Change the fraction to an equivalent fraction with denominator 100.
-
Step 2: The numerator becomes the percentage.
Example:
`7/50` = `"7 × 2 "/"50 × 2"`= `14/100` = 14%
CISCE: Class 6
Example 1
1.60 out of 100
= `"60"/"100"`
= 60 as a percent, written as 60%.
2. `"3"/"5"` × 100%
= 60 %
CISCE: Class 6
Example 2
Express each of the following statements in the percentage form:
- 5 out of 20 eggs are bad.
- 3 children in a class of 30 are absent.
Solution:
(i) 5 out of 20 eggs are bad, which means `"5"/"20"`
And `"5"/"20"` = `"5 × 5 "/"20 × 5"`= `"25"/"100"` = 25%
∴ 25% eggs are bad.
(ii) 3 children out of 30 are absent is written as `"3"/"30"`
And `"3"/"30"` = `"1"/"10"`= `"10"/"100"` = 10%
∴ 10% children are absent.
CISCE: Class 6
Real-Life Examples
-
If an exam is of 100 marks and Geeta scores 83, she scored 83% marks.
-
If Rohit scored 67%, it means he got 67 marks out of 100.
CISCE: Class 6
Key Points Summary
-
"Percent" means "out of 100".
-
The symbol % represents percentage.
-
Convert fractions to percentages by making the denominator 100 and the numerator the percentage.
-
Visualising percentages with grids and tables helps in understanding.
-
Percentages are useful to compare parts of a whole easily.
Test Yourself
Shaalaa.com | What is Percentage?
to track your progress
Related QuestionsVIEW ALL [312]
When you design your healthy diet, you want to make sure that you meet the dietary requirements to help you grow into a healthy adult. As you plan your menu, follow the following guidelines
- Calculate your ideal weight as per your height from the table given at the end of this question.
- An active child should eat around 55.11 calories for each kilogram desired weight.
- 55 per cent of calories should come from carbohydrates. There are 4 calories in each gram of carbohydrates.
- 15 per cent of your calories should come from proteins. There are 4 calories in each gram of proteins.
- 30 per cent of your calories may come from fats. There are 9 calories in each gram of fat.
Following is an example to design your own healthy diet.
Example
- Ideal weight = 40 kg.
- The number of calories needed = 40 × 55.11 = 2204.4
- Calories that should come from carbohydrates = 2204.4 × 0.55 = 1212.42 calories.
Therefore, required quantity of carbohydrates = `1212.42/4` = 303.105 g = 300 g. (approx) - Calories that should come from proteins = 2204.4 × 0.15 = 330.66 calories.
Therefore, required quantity of protein = `330.66/4` g = 82.66 g. - Calories that may come from fat = 2204.4 × 0.3 = 661.3 calories.
Therefore, required quantity of fat = `661.3/9` g = 73.47 g.
Answer the Given Questions
- Your ideal desired weight is ______ kg.
- The quantity of calories you need to eat is ______.
- The quantity of protein needed is ______ g.
- The quantity of fat required is ______ g.
- The quantity of carbohydrates required is ______ g.
| Ideal Height and Weight Proportion | |||||
| Men | Women | ||||
| Height | Weight | Height | Weight | ||
| Feet | cm | Kilograms | Feet | cm | Kilograms |
| 5’ | 152 | 48 | 4’7” | 140 | 34 |
| 5’1” | 155 | 51 | 4’8” | 142 | 36 |
| 5’2” | 157 | 54 | 4’9” | 145 | 39 |
| 5’3” | 160 | 56 | 4’1” | 147 | 41 |
| 5’4” | 163 | 59 | 4’11” | 150 | 43 |
| 5’5” | 165 | 62 | 5’ | 152 | 45 |
| 5’6” | 168 | 65 | 5’1” | 155 | 48 |
| 5’7” | 170 | 67 | 5’2” | 157 | 50 |
| 5’8” | 173 | 70 | 5’3” | 160 | 52 |
| 5’9” | 175 | 73 | 5’4” | 163 | 55 |
| 5’10” | 178 | 75 | 5’5” | 165 | 57 |
| 5’11” | 180 | 78 | 5’6” | 168 | 59 |
| 6’ | 183 | 81 | 5’7” | 170 | 61 |
| 6’1” | 185 | 84 | 5’8” | 173 | 64 |
| 6’2” | 188 | 86 | 5’9” | 175 | 66 |
| 6’3” | 191 | 89 | 5’10” | 178 | 68 |
| 6’4” | 193 | 92 | 5’11” | 180 | 70 |
