Percentage Increase and Decrease

In mathematics, understanding percentages is a crucial skill and it becomes increasingly important when solving various problems in everyday life as well as academic scenarios. These problems often involve adjustments such as increasing or decreasing quantities. In Class 6, students begin to explore this concept in more depth, and it is usually connected to the idea of ratio and proportion. This explanation will delve deeper into understanding percentage increase and decrease and how to practically apply these in solving problems.

Understanding percentages

Before we talk about increase and decrease, it's important to understand what a percentage is. A percentage is a way of expressing a number as a part of a whole. It's a ratio with a denominator of 100. The word 'percent' means 'per hundred', or one part per hundred.

For example:

• 50% means 50 out of 100.
• 25% means 25 out of 100.

In mathematical terms:

    50% = 50/100 = 0.5
    25% = 25/100 = 0.25

Percentage increase

When we talk about "percentage increase," we mean how much a quantity increases compared to its original value, expressed as a percentage.

The formula for percentage increase is as follows:

    Percentage increase = (Increase in price / Original price) × 100

Let us understand this with an example:

Suppose you scored 70 marks in your first exam and 84 marks in the second exam. You want to know the percentage increase in your marks.

First, find the increase in score:

Increase = 84 – 70 = 14

Next, apply the formula:

    Percentage increase = (14 / 70) × 100
                       = 0.2 × 100
                       = 20%

So, your score increased by 20% from the first test to the second test.

Percentage decrease

When we talk about "percentage decrease," we mean how much a quantity decreases compared to its original value, expressed as a percentage.

The formula for percentage decrease is:

    Percentage reduction = (Reduction in price / Original price) × 100

Consider an example:

A shirt originally cost $50, but now costs $40. You want to find the percentage decrease in the price.

First, find the reduction in price:

Subtraction = 50 – 40 = 10

Next, apply the formula:

    Percentage decrease = (10 / 50) × 100
                       = 0.2 × 100
                       = 20%

This means the price of the shirt decreased by 20%.

Working with ratios in percentages

A ratio is a way to directly compare two quantities. When we discuss percentage increase and decrease in relation to ratios, we think about how one value changes relative to another.

For example, let's say the ratio of apples and grapes in a basket was initially 2:3. If the number of apples increases by 50%, our new ratio can be found by first increasing the amount of apples and then making a new ratio.

    Original number of apples = 2x (for some quantity x)
    Number of apples after 50% increase = 2x + 0.5 * 2x = 3x
    New ratio of apples and grapes = 3x:3 = 1:1

Thus, ratios help in comparing changes both visually and mathematically.

Real-life applications

There are many real-world applications of these percentage calculations. Let's consider a few scenarios:

• Shopping discounts: If a product is on sale for 30% off, and the original price is $80, you can calculate the new price and savings.

        Discount = 30% of $80 = (30/100) × 80 = $24
        New price = $80 - $24 = $56
    

• Population growth: If the population of a city grows from 20,000 at a rate of 5% per year, the growth can be calculated for each year.
• Salary: When companies give a percentage increase in salaries, it is important to understand what impact this has on the individual salary.

Practice problems

Now, let's practice solving problems involving percentage increase and decrease:

1. If a population of 1,500 increases by 10%, what will be the new population?

           Increase = (10/100) × 1500 = 150
           New population = 1500 + 150 = 1650
       

2. A car worth $22,000 depreciates in value by 15% in one year. What will be its value after one year?

           Deficiency = (15/100) × 22000 = 3300
           Value after one year = 22000 – 3300 = 18700
       

Conclusion

Mastering percentage increase and decrease is beneficial and important not only in math, but also in everyday tasks and decisions. It helps you become smarter in financial decisions, shopping deals, and understanding real-world data. Be sure to practice with a variety of problems to strengthen your understanding and ability to calculate these changes quickly and accurately.

Comments