Grade 6
  1. Number System  1.1. Whole Numbers  1.1.1. Place Value and Face Value  1.1.2. Comparing and Ordering Numbers  1.1.3. Rounding Numbers  1.1.4. Properties of Whole Numbers (Associative, Commutative, Distributive)  1.2. Integers  1.2.1. Introduction to Integers  1.2.2. Addition and Subtraction of Integers  1.2.3. Multiplication and Division of Integers  1.2.4. Properties of Integer Operations  1.3. Fractions  1.3.1. Types of Fractions  1.3.2. Equivalent Fractions  1.3.3. Simplification of Fractions  1.3.4. Addition and Subtraction of Fractions  1.3.5. Multiplication and Division of Fractions  1.3.6. Comparing and Ordering Fractions  1.4. Decimals  1.4.1. Understanding Decimals  1.4.2. Conversion between Fractions and Decimals  1.4.3. Addition and Subtraction of Decimals  1.4.4. Multiplication and Division of Decimals  1.4.5. Comparing and Ordering Decimals
  2. Algebra  2.1. Basics of Algebra  2.1.1. Variables and Constants  2.1.2. Expressions and Equations  2.1.3. Algebraic Terms and Coefficients  2.2. Solving Simple Equations  2.2.1. Balancing Equations  2.2.2. Solving One-Step Equations  2.2.3. Solving Two-Step Equations  2.3. Patterns and Sequences  2.3.1. Identifying Patterns  2.3.2. Arithmetic Sequences
  3. Ratio and Proportion  3.1. Ratios  3.1.1. Understanding Ratios  3.1.2. Equivalent Ratios  3.1.3. Simplifying Ratios  3.2. Proportion  3.2.1. Introduction to Proportion  3.2.2. Direct and Inverse Proportions  3.3. Percentages  3.3.1. Converting Ratios to Percentages  3.3.2. Percentage Increase and Decrease  3.3.3. Discount and Profit Calculations  3.3.4. Simple Interest Calculations in Percentages in Ratio and Proportion
  4. Geometry  4.1. Basic Geometric Shapes  4.1.1. Points, Lines, and Angles  4.1.2. Types of Angles  4.1.3. Intersecting and Parallel Lines  4.2. Triangles  4.2.1. Types of Triangles  4.2.2. Properties of Triangles  4.2.3. Sum of Angles in a Triangle  4.2.4. Congruence of Triangles  4.3. Quadrilaterals  4.3.1. Types of Quadrilaterals  4.3.2. Properties of Quadrilaterals  4.4. Circles  4.4.1. Radius and Diameter  4.4.2. Circumference and Area  4.4.3. Arcs and Chords  4.4.4. Sector and Segment
  5. Mensuration  5.1. Perimeter  5.1.1. Perimeter of Simple Shapes  5.2. Area  5.2.1. Area of Rectangles and Squares  5.2.2. Area of Triangles and Parallelograms  5.2.3. Area of Composite Figures  5.2.4. Area of Trapezium  5.3. Volume  5.3.1. Volume of Cubes and Cuboids  5.3.2. Volume of Cylinders  5.3.3. Volume of Cones  5.3.4. Surface Area of Simple Solids
  6. Data Handling  6.1. Introduction to Data  6.1.1. Types of Data  6.1.2. Organizing Data  6.1.3. Frequency Distribution  6.2. Graphs and Charts  6.2.1. Bar Graphs  6.2.2. Line Graphs  6.2.3. Pictographs  6.2.4. Pie Charts  6.3. Mean, Median, and Mode  6.3.1. Calculating Mean  6.3.2. Finding Median  6.3.3. Identifying Mode  6.3.4. Range of Data in Mean, Median, and Mode
  7. Probability  7.1. Basics of Probability  7.1.1. Understanding Probability  7.1.2. Probability of Simple Events  7.1.3. Experimental and Theoretical Probability
  8. Practical Geometry  8.1. Construction of Shapes  8.1.1. Constructing Triangles  8.1.2. Constructing Quadrilaterals  8.1.3. Constructing Circles and Arcs  8.2. Symmetry  8.2.1. Line of Symmetry  8.2.2. Rotational Symmetry  8.2.3. Translational Symmetry

Grade 6 ↓


Number System


A number system is a way of representing and working with numbers in mathematics. It enables us to write numbers, perform arithmetic operations, and understand the different types of numbers we encounter in everyday life. In this lesson, we will learn about the meaning of numbers in mathematics. You will explore the number system, including types of numbers, basic operations, properties, and more.

What is the number system?

The number system defines a set of values used to represent quantities. It uses symbols to represent numbers. Different cultures developed their own number systems, the most common being the decimal system, which is written in base 10. Also known as, which is the one we use most often.

Decimal number system

The decimal number system is the most commonly used number system. It has 10 symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. These symbols are called digits. Each symbol in a number represents a digit. Numerals have a place value, and it is based on powers of 10.

For example, the number 452 can be split as follows:

        452 = (4 × 100) + (5 × 10) + (2 × 1)

Visualization of place values

452

In this example, 4 is in the hundreds place, 5 is in the tens place, and 2 is in the ones place, which helps us understand the value of each digit of the number.

Types of numbers

Natural numbers

These are the numbers commonly used for counting. They start at 1 and go on to infinity: 1, 2, 3, 4, and so on.

Whole numbers

Whole numbers include all natural numbers along with 0. So, 0, 1, 2, 3, 4, etc. are whole numbers.

Integers

Integers are all whole numbers, but they also include negative numbers. For example, ... -3, -2, -1, 0, 1, 2, 3, ... are integers.

Rational numbers

A rational number can be expressed as a fraction or ratio of two integers. For example, 1/2 , 2/3 and 4/1 are rational numbers.

Irrational numbers

These numbers cannot be expressed as simple fractions. Their decimal expansions are non-recursive and non-terminating. Examples include √2 , π .

Operations in number system

Add

Addition is the process of finding the sum of two or more numbers or quantities. For example:

       23
    + 56
    ,
       79

Subtraction

Subtraction is the process of finding the difference between numbers. For example:

       78
    - 23
    ,
       55

Multiplication

Multiplication involves adding like groups together. Here's how you can multiply:

       12
    × 3
    ,
       36

Division

Division means splitting into equal parts or groups. This is the result of "fair division". For example:

      34 ÷ 2 = 17

Properties of numbers

Commutative property

This property states that the order does not matter for addition or multiplication.

        a + b = b + a
        a × b = b × a

Associative property

The way the numbers are grouped has no effect on the sum or product.

        (a + b) + c = a + (b + c)
        (a × b) × c = a × (b × c)

Distributive property

This property combines addition and multiplication.

        a × (b + c) = a × b + a × c

Identity property

Adding 0 or multiplying by 1 leaves the number unchanged.

        a + 0 = a
        a × 1 = a

Further elaboration with examples

Example: Understanding decimals

Decimals are fractions of base ten. For example, 0.75 is 75/100.

        0.75 = 7/10 + 5/100

Examples: Fractions

Using fractions is a way to show division between numbers. For example:

        3/4 means 3 parts out of a total of 4 equal parts.
3/4 of the rectangle is purple

Special types of numbers

Prime numbers

A prime number is a number greater than 1 that has no positive divisors other than 1 and itself. Example: 2, 3, 5, 7, 11.

Composite numbers

These are numbers that have more than two factors. For example, 4, 6, 8, and 10 are composite numbers.

Even and odd numbers

Even numbers are divisible by 2. Odd numbers are not. For example, 2, 4, 6 are even while 1, 3, 5 are odd.

This introduction to the number system will help you build a strong foundation for learning and exploring the world of numbers. With numbers, you can model real-world problems, perform calculations, and delve into deeper mathematical concepts can be done.


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Number System

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