Percentages are a special way of expressing fractions with a denominator of 100. The word "percent" means "per hundred," so 45% means 45 out of 100. Percentages are used everywhere — discounts, grades, statistics, and probability all rely on this concept.

Converting between percentages, decimals, and fractions is an essential skill. To convert a percentage to a decimal, divide by 100 (move the decimal two places left): 75% = 0.75. To convert to a fraction, put the percentage over 100 and simplify: 75% = 75/100 = 3/4.

Finding a percentage of a number is a common real-world calculation. To find 20% of 80, convert 20% to 0.20 and multiply: 0.20 × 80 = 16. Understanding this process helps with calculating tips, discounts, taxes, and many other practical situations.

Percentage increase and decrease problems require understanding the original amount as 100%. A 25% increase means the new amount is 125% of the original. A 25% decrease means the new amount is 75% of the original. These concepts are fundamental to understanding growth, change, and comparison.