Percentages: Foundations
[Video Placeholder - Introduction to percentages]
Duration: 6:15
Understanding Percentages
A percentage is a ratio that compares a number to 100. The word "percent" means "per hundred."
Key Conversions
• To convert a percentage to a decimal: divide by 100 (or move decimal 2 places left)
• To convert a decimal to a percentage: multiply by 100 (or move decimal 2 places right)
• To convert a fraction to a percentage: divide numerator by denominator, then multiply by 100
Example 1: Basic Percentage Calculation
What is 25% of 80?
Method 1: Convert to decimal and multiply
25% = 0.25
0.25 × 80 = 20
Method 2: Use fraction form
25/100 × 80 = (25 × 80)/100 = 2000/100 = 20
Answer: 20
Finding Percentages
Example 2: What percent is one number of another?
18 is what percent of 90?
Step 1: Set up the equation: (Part/Whole) × 100%
(18/90) × 100%
Step 2: Simplify fraction: 18/90 = 0.2
Step 3: Multiply by 100%: 0.2 × 100% = 20%
Answer: 20%
Percentage Increase/Decrease
Example 3: Percentage Increase
A $50 item is on sale for $65. What is the percentage increase?
Step 1: Find amount of increase: $65 - $50 = $15
Step 2: Divide increase by original amount: $15/$50 = 0.3
Step 3: Convert to percentage: 0.3 × 100% = 30%
Answer: 30% increase
Example 4: Percentage Decrease
A computer's price dropped from $800 to $680. What is the percentage decrease?
Step 1: Find amount of decrease: $800 - $680 = $120
Step 2: Divide decrease by original amount: $120/$800 = 0.15
Step 3: Convert to percentage: 0.15 × 100% = 15%
Answer: 15% decrease
Reverse Percentage Problems
Example 5: Finding Original Amount
After a 20% discount, a book costs $24. What was the original price?
Method 1: If 20% discount, then 80% of original price = $24
0.8 × Original = 24
Original = 24 ÷ 0.8 = $30
Method 2: Set up equation
Original - (0.20 × Original) = 24
0.80 × Original = 24
Original = 24 ÷ 0.80 = $30
Answer: The original price was $30