Percentage

Percentage is an important concept in mathematics used to compare quantities. The word "percent" means "per hundred," derived from the Latin phrase "per centum." A percentage is a dimensionless ratio, expressed as a fraction of 100. It is often used to compare the relative size or importance of two or more quantities. The symbol for percentage is "%."

For example, if you say 50%, it means 50 out of 100 or half. Percentages are widely used in everyday life. They are important in finance, statistics, and many other fields. Percentages are important to understand because they help us easily convey information about proportions, increase, decrease, and comparison in a relative way.

Understanding basic percentage concepts

To understand percentages, let's start with some basic concepts and examples. Consider a simple scenario where we have a pie chart that represents a whole pie.

In the pie chart above, 25% of the pie is filled with orange color, and 75% is filled with grey color. This shows a simple percentage division. When we say 25%, it means that 25 out of every 100 parts are orange.

Calculating percentages

Use the formula to find the percentage of a part compared to a whole:

Percentage (%) = (Part / Whole) * 100

Let's look at a calculation example:

Imagine that you scored 45 out of a total of 50 marks in an exam. To calculate the percentage of marks obtained, you use the following formula:

Percentage (%) = (45 / 50) * 100 = 90%

So, you scored 90% marks in your exam.

This calculation tells us that when comparing 45 with 50, 45 represents 90% of 50.

Different examples of percentages

Example 1: Percent as a part of a whole

Suppose there are 40 students in a class. If 10 students have blue books, you can find the percentage of students who have blue books by this formula:

Percentage of students with blue books = (10 / 40) * 100 = 25%

This means that 25% of the students in the class have blue books.

Example 2: Percentage increase

Let's say your favorite product cost $100 last month and costs $120 this month. To calculate the percentage increase in cost, use this formula:

Percentage Increase = ((New Price - Old Price) / Old Price) * 100

Let's do the calculation:

Percentage Increase = ((120 - 100) / 100) * 100 = 20%

The price increased by 20% this month compared to last month.

Example 3: Percentage decrease

Suppose the bird population was 200 last year, but this year it decreased to 180. To find the percentage decrease in the bird population, apply this formula:

Percentage Decrease = ((Old Number - New Number) / Old Number) * 100

Let's do the calculation:

Percentage Decrease = ((200 - 180) / 200) * 100 = 10%

The bird population declined by 10% this year.

Using percentages in comparison

Percentages are also used to compare different items. This helps us understand how much of one quantity is of another. Let us consider some examples.

Example 4: Comparing two quantities

If person A has $50 and person B has $75, you want to know what percentage of the money person B has is of person A's money.

Percentage = (Person B's Money / Person A's Money) * 100

Calculation of Percentage:

Percentage = (75 / 50) * 100 = 150%

Person B's wealth is 150% of person A's wealth.

Fractions, decimals and percentages

Percentages can also be converted between fractions and decimals. Let's learn how.

Converting percentages to decimals

To convert a percentage to a decimal, divide by 100. For example, to convert 45% to a decimal:

Decimal = 45 / 100 = 0.45

Converting decimals to percentages

To convert a decimal to a percentage, multiply by 100. Converting 0.76 to a percentage:

Percentage = 0.76 * 100 = 76%

Converting percentage to fraction

To convert a percentage to a fraction, express the percentage as a fraction with a denominator of 100 and simplify. For example, 60% as a fraction:

Fraction = 60 / 100 = 3/5 (after simplification)

Converting a fraction to a percentage

To convert a fraction to a percentage, divide the top by the bottom and then multiply by 100. Converting 3/4 to a percentage:

Percentage = (3 / 4) * 100 = 75%

It is very important to understand the relationship between fractions, decimals, and percentages. This provides a more comprehensive understanding of percentages than wholes and parts.

Importance of percentages in real life

Percentages aren't just important in math class; they're also a vital part of real-life situations. Here are several areas where percentages come into play:

• Sales and discounts: When making a purchase, percentages are used to calculate discounts. For example, a 20% discount on a $50 item reduces the price by $10.
• Interest rates: Banks use interest rates to determine how much extra you'll pay on a loan or earn on savings.
• Grades and marks: Students often receive marks and understand their performance based on percentage of marks.
• Statistics: Statistics uses percentages to interpret data more meaningfully, such as what percentage of people like a particular product.

Custom question

1. If 200 students are enrolled in a course and 150 passed the final examination, then what percentage of students passed?
2. You buy a product for $250 and get a 15% discount. How much do you have to pay?
3. The price of a car was $20,000 last year and increased to $22,000 this year. By what percent did the price of the car increase?
4. If 60% of a number is 120, then what is the original number?

Conclusion

Percentages are a fundamental aspect of mathematics and are crucial to understanding and comparing quantities. They allow us to express parts of a whole and efficiently analyze increases or decreases. Becoming familiar with percentages, fractions, and decimals enhances the ability to interpret the various data forms encountered in real life. Through understanding and practice, one can confidently use percentages in a number of scenarios, from academic contexts to everyday financial matters. This guide should serve as a foundation for anyone looking to understand and master percentages and their applications.

Comments