Grade 8
  1. Number Systems  1.1. Rational Numbers  1.2. Irrational Numbers  1.3. Real Numbers  1.4. Properties of Real Numbers  1.4.1. Commutative Property  1.4.2. Associative Property  1.4.3. Distributive Property  1.5. Representation on the Number Line  1.6. Operations on Real Numbers  1.6.1. Addition and Subtraction  1.6.2. Multiplication and Division  1.7. Rationalization  1.8. Exponents and Powers  1.9. Square Roots and Cube Roots
  2. Algebra  2.1. Algebraic Expressions  2.2. Identities and Simplification  2.2.1. Multiplying Binomials  2.2.2. Using Algebraic Identities  2.3. Factorization  2.3.1. Common Factors  2.3.2. Factorization by Grouping  2.3.3. Factorization of Trinomials  2.3.4. Special Products  2.4. Linear Equations in One Variable  2.4.1. Solving Linear Equations  2.4.2. Word Problems on Linear Equations
  3. Geometry  3.1. Understanding Quadrilaterals  3.1.1. Properties of Quadrilaterals  3.1.2. Types of Quadrilaterals  3.1.2.1. Parallelogram  3.1.2.2. Rectangle  3.1.2.3. Square  3.1.2.4. Rhombus  3.1.2.5. Trapezium  3.2. Constructions  3.2.1. Constructing Quadrilaterals  3.2.2. Constructing Bisectors  3.2.3. Constructing Angles  3.2.4. Constructing Triangles  3.3. Symmetry and Transformations  3.3.1. Reflection  3.3.2. Rotation  3.3.3. Translation  3.3.4. Symmetry in Patterns
  4. Mensuration  4.1. Area and Perimeter  4.1.1. Perimeter of Polygons  4.1.2. Area of Triangles  4.1.3. Area of Quadrilaterals  4.1.4. Area of Circles  4.2. Surface Area and Volume  4.2.1. Cubes  4.2.2. Cuboids  4.2.3. Cylinders  4.2.4. Cones  4.2.5. Spheres
  5. Data Handling  5.1. Organizing Data  5.2. Frequency Distribution Tables  5.3. Graphical Representation of Data  5.3.1. Bar Graphs  5.3.2. Histograms  5.3.3. Pie Charts  5.3.4. Line Graphs (added)  5.4. Probability  5.4.1. Introduction to Probability  5.4.2. Experimental Probability
  6. Coordinate Geometry  6.1. Cartesian Plane  6.2. Plotting Points  6.3. Coordinate System  6.4. Distance Between Points  6.5. Applications of Coordinate Geometry
  7. Introduction to Graphs  7.1. Linear Graphs  7.2. Applications of Graphs  7.3. Distance-Time Graphs  7.4. Speed-Time Graphs
  8. Comparing Quantities  8.1. Ratio and Proportion  8.2. Percentage  8.2.1. Increase and Decrease Percent  8.2.2. Discount in Percentage  8.2.3. Profit and Loss in Percentage  8.2.4. Simple Interest  8.2.5. Compound Interest
  9. Exponents and Powers  9.1. Laws of Exponents  9.2. Negative Exponents  9.3. Standard Form  9.4. Applications of Exponents
  10. Introduction to Squares and Square Roots  10.1. Properties of Square Numbers  10.2. Finding Square Roots  10.2.1. Prime Factorization Method  10.2.2. Division Method  10.3. Estimating Square Roots
  11. Introduction to Cubes and Cube Roots  11.1. Properties of Cube Numbers  11.2. Finding Cube Roots  11.2.1. Prime Factorization Method in Finding Cube Roots

Grade 8 → Number Systems ↓


Representation on the Number Line


In mathematics, the number line is a straight horizontal line that represents numbers as dots placed in an equally spaced sequence. The number line is not only fundamental to simple arithmetic but also forms the basis for understanding more complex mathematical concepts. Understanding the representation on the number line helps in understanding the essential idea of positive numbers, negative numbers, the concept of zero, and intervals, as well as other aspects.

Understanding the number line

The number line is usually drawn horizontally, and it is made up of several elements: a central point usually marked as zero, points to the right indicating positive numbers, points to the left indicating negative numbers, and evenly spaced ticks or marks indicating increments between numbers. Let's begin by examining how basic numbers are represented on a number line.

Positive numbers on the number line

In simple words, positive numbers are numbers greater than zero. They appear to the right of zero on the number line. For example, numbers like 1, 2, 3, etc. are considered positive numbers.

0 -4 -2 +3 +5

Negative numbers on the number line

Negative numbers are numbers that are less than zero. On the number line, they are placed to the left of zero. Examples of negative numbers include -1, -2, -3, and these continue to infinity in the negative direction.

0 -1 -3 +2

Importance of zero

Zero plays an important role on the number line, serving as the dividing point between positive and negative numbers. It is neither positive nor negative, but rather serves as a reference point from which all numbers are measured.

Representation of fractions on the number line

Fractions can also be represented on the number line. A fraction represents a part of a whole and is expressed in the form a/b, where a is the numerator and b is the denominator. To represent fractions on the number line, it is important to divide the space between the whole numbers into equal parts.

Example: To represent 3/4 on the number line:
- Divide the space between 0 and 1 into 4 equal sections.
- Count sections 0 to 3.
0 1 1/4 2/4 3/4

Mixed numbers on the number line

Mixed numbers are numbers that include both a whole number and a fraction. To represent a mixed number on the number line, first find the position of the whole number and then add the fractional part.

Example: To mark 2 1/2 on the number line:
- Find the 2 on the line.
- Divide the interval between 2 and 3 into two equal parts.
- Mark 2 1/2 minutes.
1 2 3 2 1/2

Decimal representation on number line

Decimals, like fractions, represent parts of a whole and can also be plotted on the number line. The decimal point allows us to express quantities that are not whole numbers, and they occupy the space between the whole numbers on the number line.

Example: To mark 2.5 on the number line:
- Identify situation 2.
- Identify situation 3.
- Find the midpoint between 2 and 3, which is 2.5.
2 3 2.5

Using the number line for arithmetic operations

The number line is not just about placing numbers; it is also a useful tool for performing arithmetic operations such as addition, subtraction, multiplication, and division. Here's how you can do that:

Add

To add two numbers using a number line, start at the point of the first number and move to the right as far as the second number.

Example: 3 + 4
- Start at 3 on the number line.
- Walk 4 steps to the right.
- You get off at 7.

Subtraction

Subtraction is the opposite of addition. To subtract on the number line, move to the left.

Example: 7 - 3
- Start at 7 on the number line.
- Walk 3 steps to the left.
- You land on 4.

Multiplication and division

Multiplication and division are basically repeated addition and subtraction on the number line.

Multiplication Example: Calculating 3 x 2
- Start at 0 and jump by 3 twice.
- You get off on 6.

Division Example: Calculating 6 ÷ 3
- Start at 6 and jump backwards 3 times until you reach 0.
- You make 2 jumps.

Conclusion

The number line is a powerful tool in mathematics for visualizing numbers, fractions, decimals, and performing various arithmetic operations. By understanding the number line and practicing plotting different types of numbers, we can develop a deep, visual understanding of mathematical concepts. This representation helps to understand how numbers relate to each other and simplifies operations with both whole and fractional numbers.


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Representation on the Number Line

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