Percentages are a fundamental part of everyday life, from calculating discounts while shopping to understanding statistics at work or in school. Knowing How To Get The Percentage Of A Number is a crucial skill for anyone looking to navigate the numerical world with confidence. This guide breaks down the concept of percentages, provides clear formulas, and offers practical examples to help you master percentage calculations.
Understanding Percentages: The Basics
At its core, a percentage is simply a way of expressing a fraction or a ratio as a part of 100. The word “percent” literally means “per hundred”. So, when you see a percentage like 25%, it means 25 out of every 100, or 25/100. This can also be represented as the decimal 0.25.
Percentages make it easier to compare proportions and understand relative amounts. Instead of dealing with fractions or decimals directly, percentages provide a standardized way to express these values in relation to a whole of 100.
The Fundamental Percentage Formula
Most percentage problems can be solved using variations of a single basic formula. Thinking of it in its simplest form, we can express it as:
*(Part / Whole) 100 = Percentage**
Where:
- Part: The specific amount you are interested in.
- Whole: The total amount or the reference value.
- Percentage: The proportion of the part relative to the whole, expressed as a percentage.
From this basic formula, we can derive formulas to solve three common types of percentage problems.
1. Calculating a Percentage of a Number: Finding the “Part”
This is perhaps the most common percentage calculation. You want to find out what a certain percentage represents out of a given total. For example, “What is 20% of 50?”.
Formula: Percentage (%) * Whole = Part
To use this formula, you first need to convert the percentage into a decimal. To do this, divide the percentage by 100 or simply move the decimal point two places to the left.
Example: What is 20% of 50?
- Convert the percentage to a decimal: 20% ÷ 100 = 0.20
- Apply the formula: 0.20 * 50 = Part
- Calculate: 0.20 * 50 = 10
- Answer: 20% of 50 is 10.
Step-by-step breakdown:
- Identify the Percentage: In this case, it’s 20%.
- Identify the Whole: Here, it’s 50.
- Convert Percentage to Decimal: Divide 20 by 100 to get 0.20.
- Multiply: Multiply the decimal (0.20) by the whole number (50).
- Result: The result, 10, is the percentage of the number.
Real-world application: Imagine you want to tip 15% on a restaurant bill of $40. To calculate the tip amount, you would find 15% of 40: 0.15 * 40 = $6.
2. Finding What Percentage One Number Is of Another: Determining the “Percentage”
In this scenario, you know the “Part” and the “Whole” and want to find out what percentage the “Part” represents of the “Whole”. For example, “What percentage of 80 is 20?”.
Formula: (Part / Whole) * 100 = Percentage (%)
Example: What percentage of 80 is 20?
- Identify the Part and the Whole: Part = 20, Whole = 80.
- Apply the formula: (20 / 80) * 100 = Percentage (%)
- Calculate the division: 20 / 80 = 0.25
- Multiply by 100: 0.25 * 100 = 25
- Answer: 20 is 25% of 80.
Step-by-step breakdown:
- Identify the Part: This is 20.
- Identify the Whole: This is 80.
- Divide: Divide the part (20) by the whole (80).
- Multiply by 100: Multiply the result (0.25) by 100 to convert it to a percentage.
- Result: The result, 25%, is the percentage one number is of another.
Real-world application: Suppose you scored 75 out of 100 points on a test. To find your percentage score, you would calculate (75 / 100) * 100 = 75%.
3. Finding the “Whole” When You Know the “Part” and the “Percentage”
Sometimes, you know a percentage and the value it represents (“Part”), and you need to find the original “Whole”. For instance, “30 is 60% of what number?”.
Formula: Part / Percentage (%) = Whole
Remember to convert the percentage to a decimal before using it in the formula.
Example: 30 is 60% of what number?
- Identify the Part and Percentage: Part = 30, Percentage = 60%.
- Convert the percentage to a decimal: 60% ÷ 100 = 0.60
- Apply the formula: 30 / 0.60 = Whole
- Calculate: 30 / 0.60 = 50
- Answer: 30 is 60% of 50.
Step-by-step breakdown:
- Identify the Part: This is 30.
- Identify the Percentage: This is 60%.
- Convert Percentage to Decimal: Divide 60 by 100 to get 0.60.
- Divide: Divide the part (30) by the decimal percentage (0.60).
- Result: The result, 50, is the whole number.
Real-world application: Imagine a store is offering a 25% discount, and you save $15 on an item. To find the original price, you would calculate $15 / 0.25 = $60.
Converting Between Percentages and Decimals: Essential Skills
As you’ve seen, converting between percentages and decimals is crucial for percentage calculations. Here’s a quick recap:
Percentage to Decimal:
- Divide by 100: Take the percentage value and divide it by 100.
- Move Decimal Point Left: Alternatively, move the decimal point two places to the left.
Example: 45% = 45 / 100 = 0.45
Decimal to Percentage:
- Multiply by 100: Take the decimal value and multiply it by 100.
- Move Decimal Point Right: Alternatively, move the decimal point two places to the right and add the percent sign (%).
Example: 0.78 = 0.78 * 100 = 78%
Practice Problems: Putting It All Together
Let’s solidify your understanding with a few more examples:
-
What is 35% of 200?
- Convert 35% to decimal: 0.35
- Multiply: 0.35 * 200 = 70
- Answer: 70
-
What percent of 75 is 15?
- Divide: 15 / 75 = 0.20
- Convert to percentage: 0.20 * 100 = 20%
- Answer: 20%
-
12 is 4% of what number?
- Convert 4% to decimal: 0.04
- Divide: 12 / 0.04 = 300
- Answer: 300
Conclusion: Mastering Percentage Calculations
Understanding how to get the percentage of a number and the different types of percentage problems empowers you to solve a wide range of practical calculations. By mastering the basic formulas and practicing with examples, you’ll gain confidence in your numerical abilities and be able to apply these skills in various real-life situations. Keep practicing, and percentages will become second nature!
For further practice and to check your calculations, you can use online percentage calculators. These tools can be helpful for verifying your answers and exploring more complex percentage problems.
References
Weisstein, Eric W. “Percent.” From MathWorld — A Wolfram Web Resource.
