Percentages are one of the most fundamental concepts in mathematics, playing a crucial role in various aspects of daily life, from calculating discounts to understand statistics. In this comprehensive guide, we will explore the concept of percentage in detail, including their history, how they are calculated, real-life applications and more, Additionally, we will provide worksheets to help you master the topic through practice.
What is Percentage?
A percentage is a way of expressing a number as fraction of 100. The term 'percent' originates from the Latin phrase "per centum", meaning "by the hundred". In mathematical terms, a percentage represents a part of a whole and is often denoted by the symbol %.
Examples of Percentages:
- 50% represents half of a quantity
- 25% represents one-fourth of a quantity
- 100% represents the entire quantity
The Formula for Percentage
To calculate the percentage, apply this formula:
Percentage = (Part / whole) x 100
Example:
If you have 20 apples out of a total of 50 apples, the percentage of apples you have is:
Percentage = (Part / whole) x 100 = (20 / 50) x 100 = 40%
Converting Between Percentages, Fractions and Decimals
Understanding how to convert between percentages, fractions and decimals is essential for solving problems involving percentages.
Converting Percentages to Fractions
To convert a percentage to a fraction:
1. Remove the % sign
2. Write the number over 100
3. Simplify the fraction if possible
Examples: 25% = 25 / 100 = 1 / 4
Converting Percentages to Decimals
To convert a percentage to a decimal:
1. Remove the % sign
2. Divide the number by 100
Example: 75% = 75 / 100 = 0.75
Converting Fractions to Percentages
To convert a fraction to a percentage:
1. Divide the numerator by the denominator
2. Multiply the result by 100
Example: 3 / 4 = 0.75 x 100 = 75%
Converting Decimals to Percentages
To convert a decimal to a percentage:
1. Multiply the decimal by 100
2. Add the % sign
Example: 0.85 = 0.85 x 100 = 85%
Application of Percentages in Daily Life
Percentages are used in various fields and situations. Here are some common applications:
1. Shopping and Discounts
Percentages are commonly used in sales and discounts. For instance, a 20% discounts on a $50 item means you save $10.
Calculation: Discount Amount = Price x (Discount Percentage / 100) = 50 x (20 / 100) = 50 x 0.2 = $10
2. Finance and Investments
Percentages are crucial in understanding interest rates, returns on investment, and profit margins.
Example: Simple Interest Formula: Simple Interest = (Principal x Rate x Time) / 100
Calculation: For a principal of $ 1000 at an interest rate of 5% for 2 years:
Simple Interest = ($1000 x 5 x 2) / 100 = $ 100
3. Population and Demographics
Percentages help express demographic data, such as literacy rates of population growth.
Example: If a city has a population of 1 000 000 and 30% are children, the number of children is:
Number of children = Total population x (percentage / 100) = 1 000 000 x (30 / 100)
= 1 000 000 x 0.3 = 300 000
4. Academic Performance
Grades and scores are often expressed as percentages.
Example: A student who scores 45 out of 50 on a test has percentage of:
Percentage = (Part / Whole) x 100 = (45 / 50) x 100 = 90%
5. Data Analysis and Statistics
Percentage are used to represent proportions in charts, graphs and statistical analysis.
Example: If 60 out of 200 surveyed people prefer coffee, then:
Percentage = (Part / Whole) x 100 = (60 / 200) x 100 = 30%
Percentage Increase and Decrease
Percentage Increase
To calculate the percentage increase:
Example: If the price of a product increases from $50 to $75:
Solution:
Percentage Increase = (New Value - Original Value / Original Value) x 100
1. Subtract the original value from the new value:
75 - 50 = 25
2. Divide the difference by the original value:
25 / 50 = 0.5
3. Multiply by 100 to convert to a percentage:
0.5 x 100 = 50%
The percentage increase is 50%
Percentage Decrease
To calculate the percentage decrease:
Example: IF the price of a product decreases from $80 to $60:
Solution:
Percentage Decrease = (Original Value - New Value / Original Value) x 100
1. Subtract the new value from the original value:
80 - 60 = 20
2. Divide the difference by the original value:
20 / 80 = 0.25
3. Multiply by 100 to convert to a percentage:
0.25 x 100 = 25%
The percentage decrease is 25%
Conclusion
Understanding percentages is a vital skill with countless applications in real life, from managing finances to interpreting data. By mastering the concepts, formulas and techniques outlines in this guide, you will be well-equipped to tackle any problem involving percentages. Don't forget to practice using the practice worksheets to strengthen your skills.
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