## Introduction

Percentage increase refers to the measure of how much a value has increased in proportion to its original amount expressed in percentage. This calculation is an important skill in everyday life that is useful in a wide range of fields, from finance to science. By knowing how to find percentage increases accurately, one can determine price increases, population growth rates, and even calculate investment returns.

## Step-by-Step Guide

The formula used to find percentage increase is (new value – original value) / original value x 100%. To illustrate this formula, imagine a product you bought for $50 is now priced at $60.

1. Subtract the original value from the new value: $60 – $50 = $10.

2. Take the result and divide it by the original value: $10 / $50 = 0.2.

3. Multiply the value by 100% to find the percentage increase: 0.2 x 100% = 20%.

Therefore, the percentage increase is 20%.

Another example could be the calculation of the percentage increase of the population of cities. If a city’s population increased from 100,000 to 120,000 in five years, one can calculate the percentage increase in the following way:

1. Subtract the original population from the new population: 120,000 – 100,000 = 20,000.

2. Dividing the result by the original value: 20,000 / 100,000 = 0.2.

3. Multiplying the value by 100% to obtain the percentage increase: 0.2 x 100% = 20%.

Therefore, the population increase of the city is 20% over the five-year period.

## Comparison between Percentage Increase and Absolute Increase

Absolute increase refers to the difference between the new value and original value. It is different from a percentage increase because it doesn’t take into account the proportion between the increase and the original amount.

For example, if an investment of $10,000 has a return of $500, the absolute increase is $500. However, to calculate the percentage increase, one needs to divide the absolute increase by the original value and multiply it by 100%, which will give you a percentage increase of 5%.

## Common Errors When Calculating Percentage Increase and How to Avoid Them

Some of the common errors people make when calculating the percentage increase are:

1. Failing to convert percentage increase into a decimal: Always ensure that you do convert the percentage increase into a decimal. For instance, a percentage increase of 10% is equivalent to 0.1.

2. Failing to subtract the original value from the new value: You need to subtract the original value from the new value for accurate calculations.

3. Confusing percentage increase with percentage difference: Percentage increase refers to the change to the original value, while percentage difference involves comparing two different values.

## Real-Life Scenarios

Percentage increase is useful in several real-life scenarios. Some of them include:

1. Sales and price change: By knowing the percentage increase, you can determine if the price of a product has increased or decreased.

2. Population growth rates: The percentage increase can determine the growth rate of a group by comparing its current size to the original size.

3. Salary increase and investment returns: One can calculate the percentage of salary increases or investment returns to determine if the increase is proportionate and worthwhile.

## Interactive Quiz

Test your knowledge on percentage increase by taking this fun quiz:

1) What formula is used to calculate percentage increase?

a. (new value – original value)

b. (new value + original value) / original value

c. (new value – original value) / original value x 100%

Answer: C.

Explanation: The formula used to calculate percentage increase is (new value – original value) / original value x 100%.

2) If an item’s price increases from $500 to $550, what is the percentage increase?

a. 10%

b. 9%

c. 11%

Answer: A.

Explanation: The price of the item has increased by $50 ($550 – $500). Using the formula, we can determine the percentage increase is (50/500) x 100% = 10%.

## Conclusion

In conclusion, knowing how to find percentage increase is an essential skill in everyday life that can be useful in determining population growth, return on investment, and sales or price fluctuations. It’s crucial to avoid common errors when calculating percentage increase and make a clear distinction from absolute increase. By following the easy steps outlined in this article, one can accurately calculate percentage increase and make informed decisions based on the results.