Understanding Percentages: Calculations and Changes

Sure! Here's a detailed, factual article about the topic "percentage" focusing on the subtopics: calculating percentages, percentage increase, percentage of a number, and percentage decrease.

Percentage

A percentage is a way of expressing a fraction or ratio of any value as a number out of 100. It is often used to express a portion of a value relative to the whole.

Calculating Percentages

Calculating percentages involves three steps:

1. Find the total or the whole.
2. Find the part that you want to express as a percentage.
3. Divide the part by the whole and multiply the result by 100.

For example, if you have a total of 100 apples and you want to find the percentage of apples that are red, you can follow these steps:

1. Identify the total number of apples, 100.
2. Count the number of red apples, let's say there are 60 red apples.
3. Divide the number of red apples (60) by the total number of apples (100) to find the ratio: 60/100 = 0.6.
4. Multiply this ratio by 100 to find the percentage: 0.6 * 100 = 60%.

The percentage of red apples is 60%.

Percentage Increase

Percentage increase is the change in a value divided by the original value, expressed as a percentage. To calculate percentage increase, follow these steps:

1. Determine the difference between the new value and the old value.
2. Divide the difference by the original value.
3. Multiply the result by 100.

For example, if the price of a book increases from $20 to $24, the percentage increase is:

1. $24 - $20 = $4.
2. $4 / $20 = 0.2.
3. 0.2 * 100 = 20%.

The percentage increase is 20%.

Percentage of a Number

To find the percentage of a number, you can use the following formula:

Percentage of a number = Number of parts / Total number of parts * 100

For example, if you have 5 parts out of 10 parts, the percentage of a number is:

5 / 10 * 100 = 50%

The percentage of 5 is 50%.

Percentage Decrease

Percentage decrease is the opposite of percentage increase. It is the difference in the value divided by the original value, expressed as a percentage. To calculate percentage decrease, follow these steps:

1. Determine the difference between the new value and the old value.
2. Divide the difference by the original value.
3. Multiply the result by -100.

For example, if the price of a book decreases from $24 to $20, the percentage decrease is:

1. $20 - $24 = -$4.
2. -$4 / $24 = -0.166666667.
3. -0.166666667 * -100 = 16.666666667%.

The percentage decrease is approximately 16.67%.

I hope this article provides a detailed explanation of the topic "percentage" and its subtopics: calculating percentages, percentage increase, percentage of a number, and percentage decrease. Let me know if you have any questions!