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:
A percentage is a way to express a number as a fraction of 100, represented by the symbol "%".
To calculate the percentage of a number, multiply the number by the percentage expressed as a decimal. For example, 20% of 50 is calculated as 50 × 0.20 = 10.
Percentage increase measures how much a value has grown over time. It's calculated by subtracting the old value from the new value, dividing by the old value, and then multiplying by 100.
To find the whole when given a part and a percentage, divide the part by the percentage (expressed as a decimal). For example, if 25% of a number is 50, the whole number is 50 / 0.25 = 200.
Percentages are commonly used to calculate discounts, interest rates, statistical data, and to compare proportions in various scenarios.
