Introduction to Percents!

Understanding percents is a fundamental skill that you’ll use in everyday life, from calculating discounts while shopping to interpreting statistics in the news. This lesson is designed to give you a good introduction and help you explore the topic with real-life applications, ensuring you build a strong foundation for more advanced mathematical concepts.

 What is a Percent?

A percent is a way to express a number as a fraction of 100. The word "percent" comes from the Latin per centum, meaning "by the hundred." It’s represented by the symbol %. For example:

• 50% means 50 out of 100, or simply half.
• 25% means 25 out of 100, which is one-quarter.

Visual Example: Imagine a pizza divided into 100 equal slices. If you eat 25 slices, you’ve eaten 25% of the pizza.

Converting Between Percents, Fractions, and Decimals

Understanding how to convert between these forms is essential for working with percents.

1. Percent to Fraction:
   Example: 75% = 75/100 = 3/4
   
   
2. Percent to Decimal:
   Example: 20% = 0.20
   
   
3. Fraction to Percent:
   Example: 1/5 = 20%
   
   
4. Decimal to Percent:
   Example: 0.85 = 85%

Basic Percentage Calculations

Let’s explore how to perform some basic percentage calculations.

Finding a Percentage of a Number:

Formula: Percentage × Number
Example: What is 30% of 200?
Calculation: 0.30 × 200 = 60

Increasing a Number by a Percentage:

Formula: Number + (Percentage × Number)
Example: Increase 150 by 10%
Calculation: 150 + (0.10 × 150) = 165

Decreasing a Number by a Percentage:

Formula: Number - (Percentage × Number)
Example: Decrease 80 by 25%
Calculation: 80 - (0.25 × 80) = 60

Real-Life Applications of Percents

Percents are everywhere! Here are some common scenarios where you’ll use percents:

1. Shopping Discounts:

• Example: You may have heard people say that they will give you a 5% discount if you purchase two T-shirts or five pants. If a jacket is marked down by 20% and the original price is $50:

• Discount: 0.20 × 50 = $10

        Sale Price: $50 - $10 = $40

2. Earnings and Jobs:

• Example: Some jobs, such as car sales, pay based on a percentage of sales. If a car salesperson earns a 10% commission on a $20,000 car sale:

• Commission: 0.10 × 20,000 = $2,000

3. Savings and Interest:

• Example: If you have a savings account, the bank may give you a 3% interest every year. Say you have $1,000 in savings account:
  
  
• Interest: 0.03 × 1,000 = $30

       Total After One Year: $1,000 + $30 = $1,030


4. Credit and Loans:

• Example: Credit card companies charge high interest of 10% to 20% depending on your credit. If you owe $500 on a credit card with a 15% interest rate:

• Interest: 0.15 × 500 = $75

       Total Owed After One Year: $500 + $75 = $575

A review of fractions and proportions may help you understand this unit. Therefore, go back and review them if time permits.