A percentage is a way of expressing a number as a fraction of 100. The term "percent" means "per hundred," and it is symbolized by the "%" sign. For example, 50% means 50 out of 100, or 50/100, which simplifies to 1/2.
Example: Converting a Fraction to a Percentage
Convert the fraction 3/4 to a percentage. Step 1: Divide 3 by 4 to get 0.75. Step 2: Multiply by 100 to get 75%. So, 3/4 = 75%.
Calculating percentages is a crucial skill in many situations, from determining the tip at a restaurant to analyzing financial data. Here's how you can calculate percentages in different scenarios:
To find the percentage of a number, multiply the number by the percentage (expressed as a decimal). For example, to find 20% of 50:
50 × 0.20 = 10
So, 20% of 50 is 10.
Percentage increase or decrease helps measure how much a value has changed over time, often used in financial analysis, price changes, and population growth. The formula for percentage change is:
Percentage Change = (New Value - Old Value) / Old Value × 100
Example: Calculating Percentage Increase
The price of a product increased from $200 to $250. What is the percentage increase? Step 1: Subtract the old price from the new price: $250 - $200 = $50. Step 2: Divide by the old price: $50 / $200 = 0.25. Step 3: Multiply by 100 to get 25%. The price increased by 25%.
Percentages are widely used in various fields, including finance, retail, and statistics. Here are some common applications:
Retail stores often offer discounts that are expressed as percentages. For example, if an item originally costs $100 and is on sale for 25% off, the discount amount is calculated as follows:
$100 × 0.25 = $25
So, the sale price is $100 - $25 = $75.
Interest rates on loans, savings accounts, and credit cards are expressed as percentages. For example, if you have a savings account with a 5% annual interest rate, this means you will earn 5% of your account balance as interest each year.
Percentages are also used to interpret data in statistics and probability. For instance, if 60 out of 100 people prefer a particular product, you can say that 60% of people prefer that product.
Solving percentage problems often involves finding one of three values: the percentage, the part (or portion), or the whole. Understanding these relationships can help you solve a variety of real-world problems.
Example: Finding the Whole
If 25% of a number is 50, what is the whole number? Step 1: Let the whole number be x. Step 2: Set up the equation: 0.25 × x = 50. Step 3: Solve for x by dividing both sides by 0.25: x = 50 / 0.25 = 200. So, the whole number is 200.
To master percentages, it's essential to practice regularly and apply these concepts in everyday situations. Here are some tips to help you get started:
