Understanding and Applying Percentages

Percentages are a fundamental concept in mathematics and are used in a wide range of real-world scenarios, from calculating discounts and interest rates to determining statistical data. This unit aims to provide a comprehensive understanding of percentages and their applications.

Definition and Conversion

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%". For example, 45% is equivalent to 45 out of 100, or 0.45 in decimal form, or 45/100 in fraction form.

Converting between percentages, fractions, and decimals is a key skill. To convert a percentage to a decimal, divide by 100. To convert a decimal to a percentage, multiply by 100. To convert a fraction to a percentage, divide the numerator by the denominator and multiply by 100.

Calculating Percentages

Of a Quantity

To find a percentage of a quantity, multiply the quantity by the percentage (in decimal form). For example, to find 20% of 50, multiply 50 by 0.20 to get 10.

Increase and Decrease

Percentage increase or decrease is used to compare changes in values. To calculate the percentage increase, subtract the original number from the new number, divide by the original number, and multiply by 100. For percentage decrease, the process is the same, but you subtract the new number from the original number.

Solving Percentage Problems

Original Amount

Sometimes, you know the final amount and the percentage that this final amount represents, and you want to find the original amount. To do this, divide the final amount by the percentage (in decimal form).

Percentage Change

Percentage change is used to compare an old value and a new value. It's calculated by subtracting the old value from the new value, dividing by the old value, and multiplying by 100.

Real-World Applications of Percentages

Percentages are used in a variety of real-world situations:

• In shops, discounts are often advertised as a percentage of the original price.
• Interest rates on savings or loans are expressed as a percentage.
• In statistics, data is often expressed as a percentage to make it easier to understand.

By understanding percentages and how to work with them, you can make sense of a wide range of mathematical and real-world situations. This unit will provide you with exercises to practice these skills and solidify your understanding.