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 → Comparing Quantities → Percentage ↓


Increase and Decrease Percent


In mathematics, especially when dealing with commercial problems, it becomes essential to understand the concept of percentage increase and percentage decrease. This topic explains how to find the percentage value increased or decreased of a given quantity. This lesson is important in solving real-world problems related to finance, sales, population studies, and much more.

What is the percentage?

The word percentage means per hundred. So, when we say 50 percent (or 50%), it means 50 out of 100, or simply put, 50/100. It is essential to understand this simple concept in order to understand the ideas of percentage increase and decrease.

The concept of percentage increase

When we talk about growth percentage, we are talking about the percentage that a number has increased compared to its original value.

Formula to calculate growth percentage

The formula for calculating growth percentage is:

 Increase percentage (%) = (Increase in price / Original price) × 100

Example of growth percentage

Suppose the price of a book was $40 last year and now it is $50. What is the increase percentage?

Here, the original price is $40. The increase in price is $50 - $40 = $10.

Use of the formula:

 Increase percentage (%) = (10 / 40) × 100 = 25%

Hence, the price is increased by 25%.

Original Price: $40 Increased price: $50

The concept of reduction percentage

In contrast, when we refer to reduction percentage, we are referring to the percentage by which a number decreases compared to its original value.

Formula to calculate reduction percentage

The formula for calculating reduction percentage is:

 Reduction percentage (%) = (Reduction in price / Original price) × 100

Example of reduction percentage

Imagine that a garment cost $100 last season and this season it sells for $70. What is the percentage reduction?

The original price is $100, and the price reduction is $100 - $70 = $30.

Apply the formula:

 Decrease percentage (%) = (30 / 100) × 100 = 30%

The price has decreased by 30%.

Original Price: $100 Reduced price: $70

More examples

  1. Example 1: Last year there were 120 students enrolled in a course. This year the enrollment increased to 156 students. Calculate the growth percentage.

    Increase in enrolment = 156 – 120 = 36 students

    Increase percentage (%) = (36 / 120) × 100 = 30%

    This shows that there has been a 30% increase in course enrolment this year.

  2. Example 2: A store had a stock of 300 units of a product, which decreased to 240 units during a sale. Find the reduction percentage.

    Decrease in stock = 300 – 240 = 60 units

    Reduction percentage (%) = (60 / 300) × 100 = 20%

    This shows that the store's stock had decreased by 20%.

Applications in real life

The concepts of percent increase and percent decrease aren't just limited to academic problems - they're important in everyday life, too. Here are a few ways:

Financial development

Investors and economists use percentage growth to express how much an investment has increased over time. If a $1000 investment grows to $1500, the growth percentage can help investors compare the profitability of different options.

Sales discount

In retail, knowing the percentage reduction helps both retailers and customers understand the effect of discounts. For example, if you know a dress was originally priced at $200 and now costs $160, calculating the reduction percentage will tell you how much the price has been reduced.

Population studies

Population studies often involve percentage growth to show how a population grows or decreases over a period of time. If a country's population was 50 million and grew to 55 million, demographers can immediately express this change as a percentage increase.

Practice problems

  1. The price of a chocolate bar was increased from $1.50 to $1.80. Calculate the percentage increase.
  2. The production of a company decreased from 1500 units to 1350 units in a month. What is the percentage decrease?
  3. The price of a book was reduced from $30 to $24 during a clearance sale. Find the percentage reduction.
  4. Due to a salary review, an employee's salary increased from $50,000 to $55,000. Find the percentage increase in salary.
  5. A certain forest area is spread over an area of 500 hectares and after one year it has reduced to 450 hectares. Find the percentage reduction in the forest area.

Solving practice problems

  1. Increase in price = $1.80 - $1.50 = $0.30 
     Increase percentage (%) = (0.30 / 1.50) × 100 = 20%
  2. Decrease in units = 1500 – 1350 = 150 units 
     Reduction percentage (%) = (150 / 1500) × 100 = 10%
  3. Decrease in price = $30 – $24 = $6 
     Decrease percentage (%) = (6 / 30) × 100 = 20%
  4. Salary increase = $55,000 – $50,000 = $5,000 
     Increase percentage (%) = (5000 / 50000) × 100 = 10%
  5. Decrease in area = 500 - 450 = 50 hectares 
     Decrease percentage (%) = (50 / 500) × 100 = 10%

Conclusion

Both percentage increase and percentage decrease provide important information when comparing changes in quantities. Whether in academic studies, financial analysis, or understanding sales trends, mastering these calculations is essential. By practicing and understanding these concepts, individuals can gain valuable skills that make analyzing and interpreting data more intuitive and straightforward. As you continue exploring the world of percentages, you will find countless applications in everyday scenarios.


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Increase and Decrease Percent

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